# Ola Bratteli's publications

1. Ola Bratteli, Conservation of estimates in quantum field theory, Comm. Pure Appl. Math. 25 (1972), 759-779.

2. Ola Bratteli, Inductive limits of finite dimensional C*-algebras, Trans. Amer. Math. Soc. 171 (1972), 195-234.

3. Ola Bratteli, Local norm convergence of states on the zero time Bose fields, Trans. Amer. Math. Soc. 188 (1974), 269-280.

4. Ola Bratteli, Structure spaces of approximately finite-dimensional C*-algebras, J. Functional Analysis 16 (1974), 192-204.

5. Ola Bratteli and Derek W Robinson, Unbounded derivations of C*-algebras, Comm. Math. Phys. 42 (1975), 253-268.

6. Ola Bratteli and Derek W Robinson, Unbounded derivations of C*-algebras. II, Comm. Math. Phys. 46 (1) (1976), 11-30.

7. Ola Bratteli, The center of approximately finite-dimensional C*-algebras, J. Functional Analysis 21 (2) (1976), 195-202.

8. Ola Bratteli and Derek W Robinson, Unbounded derivations and invariant trace states, Comm. Math. Phys. 46 (1) (1976), 31-35.

9. Ola Bratteli and Daniel Kastler, Relaxing the clustering condition in the derivation of the KMS property, Comm. Math. Phys. 46 (1) (1976), 37-42.

10. Ola Bratteli and Derek W Robinson, Unbounded derivations of von Neumann algebras, Ann. Inst. H. Poincaré Sect. A(N.S.) 25 (2) (1976), 139-164.

11. Ola Bratteli, Richard H Herman and Derek W Robinson, Quasianalytic vectors and derivations of operator algebras, Math. Scand. 39 (2) (1976), 371-381.

12. Ola Bratteli, Self-adjointness of unbounded derivations on C*-algebras, in Symposia Mathematica XX, Convegno sulle Algebre C* e loro Applicazioni in Fisica Teorica, Convegno sulla Teoria degli Operatori Indice e Teoria K, INDAM, Rome, 1975 (Academic Press, London, 1976), 137-148.

13. Ola Bratteli and Derek W Robinson, Green's functions, Hamiltonians and modular automorphisms, Comm. Math. Phys. 50 (2) (1976), 133-156.

14. Ola Bratteli and Uffe Haagerup, Unbounded derivations and invariant states, Comm. Math. Phys. 59 (1) (1978), 79-95.

15. Ola Bratteli, Richard H Herman and Derek W Robinson, Perturbations of flows on Banach spaces and operator algebras, Comm. Math. Phys. 59 (2) (1978), 167-196.

16. Ola Brattelli, Akitaka Kishimoto and Derek W Robinson, Stability properties and the KMS condition, Comm. Math. Phys. 61 (3) (1978), 209-238.

17. Ola Bratteli and George A Elliott, Structure spaces of approximately finite-dimensional C*-algebras. II, J. Funct. Anal. 30 (1) (1978), 74-82.

18. Ola Bratteli, Akitaka Kishimoto and Derek W Robinson, Ground states of quantum spin systems, Comm. Math. Phys. 64 (1) (1978/79), 41-48.

19. Ola Bratteli and Richard H Herman, Unbounded derivations of C*-algebras and corresponding dynamics, in Mathematical problems in theoretical physics, Proc. Internat. Conf., Univ. Rome, Rome, 1977, Lecture Notes in Phys. 80 (Springer, Berlin-New York, 1978), 124-133.

20. Ola Bratteli, Crossed products of UHF algebras by product type actions, Duke Math. J. 46 (1) (1979), 1-23.

21. Ola Bratteli and Derek W Robinson, Operator algebras and quantum statistical mechanics. Vol. 1. C*- and W*-algebras, algebras, symmetry groups, decomposition of states, Texts and Monographs in Physics (Springer-Verlag, New York-Heidelberg, 1979).

22. Ola Bratteli, Unbounded derivations of operator algebras, in Algèbres d'opérateurs et leurs applications en physique mathématique, Proc. Colloq., Marseille, 1977, Colloq. Internat. CNRS 274 (CNRS, Paris, 1979), 83-105.

23. Ola Bratteli and Akitaka Kishimoto, Generation of semigroups, and two-dimensional quantum lattice systems, J. Funct. Anal. 35 (3) (1980), 344-368.

24. Ola Bratteli, George A Elliott and Richard H Herman, On the possible temperatures of a dynamical system, Comm. Math. Phys. 74 (3) (1980), 281-295.

25. Ola Bratteli, Akitaka Kishimoto and Derek W Robinson, Positivity and monotonicity properties of $C_{0}$-semigroups. I, Comm. Math. Phys. 75 (1) (1980), 67-84.

26. Ola Bratteli, On the possible temperatures of a C*-dynamical system, in Mathematical problems in theoretical physics, Proc. Internat. Conf. Math. Phys., Lausanne, 1979, Lecture Notes in Phys. 116 (Springer, Berlin-New York, 1980), 397-399.

27. Ola Bratteli and Derek W Robinson, Equilibrium states of a Bose gas with repulsive interactions, J. Austral. Math. Soc. Ser. B 22 (2) (1980/81), 129-147.

28. Ola Bratteli, Generators of one-parameter groups of *-automorphisms on UHF-algebras. Quantum fields/algebras, processes, in Proc. Sympos., Univ. Bielefeld, Bielefeld, 1978 (Springer, Vienna, 1980), 167-185.

29. Ola Bratteli, George A Elliott and Akitaka Kishimoto, The temperature state space of a C*-dynamical system. I, Yokohama Math. J. 28 (1-2) (1980), 125-167.

30. Ola Bratteli and Derek W Robinson, Operator algebras and quantum-statistical mechanics. II. Equilibrium states, in Models in quantum-statistical mechanics. Texts and Monographs in Physics (Springer-Verlag, New York-Berlin, 1981).

31. Ola Bratteli and Derek W Robinson, Positive $C_{0}$-semigroups on C*-algebras, Math. Scand. 49 (2) (1981), 259-274.

32. Ola Bratteli and Palle E T Jorgensen, Unbounded derivations tangential to compact groups of automorphisms, J. Funct. Anal. 48 (1) (1982), 107-133.

33. Ola Bratteli and Palle E T Jorgensen, Unbounded *-derivations and infinitesimal generators on operator algebras, in Operator algebras and applications, Part 2, Kingston, Ont., 1980, Proc. Sympos. Pure Math. 38 (Amer. Math. Soc., Providence, R.I., 1982), 353-365.

34. Ola Bratteli and Palle E T Jorgensen, Derivations commuting with abelian gauge actions on lattice systems, Comm. Math. Phys. 87 (3) (1982/83), 353-364.

35. Ola Bratteli, A remark on extensions of quasifree derivations on the CAR-algebra, Lett. Math. Phys. 6 (6) (1982), 499-504.

36. Ola Bratteli and Derek W Robinson, Operator algebras and quantum statistical mechanics (Russian) C*- and W*-algebras, symmetry groups, decomposition of states, Translated from the English by A B Bulinskii. Translation edited and with a preface by L D Kudryavtsev ("Mir'', Moscow, 1982).

37. Ola Bratteli, Trond Digernes and Derek W Robinson, Positive semigroups on ordered Banach spaces, J. Operator Theory 9 (2) (1983), 371-400.

38. Ola Bratteli and David E Evans, Dynamical semigroups commuting with compact abelian actions, Ergodic Theory Dynam. Systems 3 (2) (1983), 187-217.

39. Ola Bratteli, George A Elliott and Palle E T Jorgensen, Decomposition of unbounded derivations into invariant and approximately inner parts, J. Reine Angew. Math. 346 (1984), 166-193.

40. Ola Bratteli, On temperature states and phase transitions in C*-dynamical systems, in Operator algebras and group representations I, Neptun, 1980, Monogr. Stud. Math. 17 (Pitman, Boston, MA, 1984), 46-59.

41. Ola Bratteli and Palle E T Jorgensen, Positive semigroups of operators, and applications: editors' introduction, Acta Appl. Math. 2 (3-4) (1984), 213-219.

42. Ola Bratteli, Palle E T Jorgensen, A Kishimoto and D W Robinson, A C*-algebraic Schoenberg theorem, Ann. Inst. Fourier (Grenoble) 34 (3) (1984), 155-187.

43. Ola Bratteli, Trond Digernes and Derek W Robinson, Relative locality of derivations, J. Funct. Anal. 59 (1) (1984), 12-40.

44. Ola Bratteli, On dynamical semigroups and compact group actions, in Quantum probability and applications to the quantum theory of irreversible processes, Villa Mondragone, 1982, Lecture Notes in Math. 1055 (Springer, Berlin, 1984), 46-61.

45. Ola Bratteli, George A Elliott and Derek W Robinson, Strong topological transitivity and C*-dynamical systems, J. Math. Soc. Japan 37 (1) (1985), 115-133.

46. Ola Bratteli and Frederick M Goodman, Derivations tangential to compact group actions: spectral conditions in the weak closure, Canad. J. Math. 37 (1) (1985), 160-192.

47. Ola Bratteli, Trond Digernes and George A Elliott, Locality and differential operators on C*-algebras. II, in Operator algebras and their connections with topology and ergodic theory, Bu?teni, 1983, Lecture Notes in Math. 1132 (Springer, Berlin, 1985), 46-83.

48. Ola Bratteli, Trond Digernes, Frederick Goodman and Derek W Robinson, Integration in abelian C*-dynamical systems, Publ. Res. Inst. Math. Sci. 21 (5) (1985), 1001-1030.

49. Ola Bratteli, George A Elliott and Derek W Robinson, The characterization of differential operators by locality: dissipations and ellipticity, Publ. Res. Inst. Math. Sci. 21 (5) (1985), 1031-1049.

50. Ola Bratteli, Frederick M Goodman and Palle E T Jorgensen, Unbounded derivations tangential to compact groups of automorphisms. II. With a comment by Klaus Thomsen, J. Funct. Anal. 61 (3) (1985), 247-294.

51. Ola Bratteli and David E Evans, Derivations tangential to compact groups: the nonabelian case, Proc. London Math. Soc. (3) 52 (2) (1986), 369-384.

52. Ola Bratteli and Akitaka Kishimoto, Derivations and free group actions on C*-algebras, J. Operator Theory 15 (2) (1986), 377-410.

53. Ola Bratteli, David E Evans, Frederick M Goodman and Palle E T Jorgensen, A dichotomy for derivations on O_n, Publ. Res. Inst. Math. Sci. 22 (1) (1986), 103-117.

54. Ola Bratteli, George A Elliott and Akitaka Kishimoto, The temperature state space of a C*-dynamical system. II, Ann. of Math. (2) 123 (2) (1986), 205-263.

55. Ola Bratteli, George A Elliott and Derek W Robinson, The characterization of differential operators by locality: classical flows, Compositio Math. 58 (3) (1986), 279-319.

56. Ola Bratteli, George A Elliott and David E Evans, Locality and differential operators on C*-algebras, J. Differential Equations 64 (2) (1986), 221-273.

57. Ola Bratteli, George A Elliott and Derek W Robinson, The characterization of differential operators by locality: C*-algebras of type I, J. Operator Theory 16 (2) (1986), 213-233.

58. Ola Bratteli, Derivations, dissipations and group actions on C*-algebras, Lecture Notes in Mathematics 1229 (Springer-Verlag, Berlin, 1986).

59. Ola Bratteli, Derivations and free group actions, in Operator algebras and mathematical physics, Iowa City, Iowa, 1985, Contemp. Math. 62 (Amer. Math. Soc., Providence, RI, 1987), 385-401.

60. Ola Bratteli and Akitaka Kishimoto, Automatic continuity of derivations on eigenspaces, in Operator algebras and mathematical physics, Iowa City, Iowa, 1985, Contemp. Math. 62 (Amer. Math. Soc., Providence, RI, 1987), 403-412.

61. Ola Bratteli and Derek W Robinson, Operator algebras and quantum statistical mechanics. 1. C*- and W*-algebras, symmetry groups, decomposition of states. Second edition. Texts and Monographs in Physics (Springer-Verlag, New York, 1987).

62. Ola Bratteli, Akitaka Kishimoto and Derek W Robinson, Embedding product type actions into C*-dynamical systems, J. Funct. Anal. 75 (1) (1987), 188-210.

63. Ola Bratteli, Frederick M Goodman, Palle E T Jorgensen and Derek W Robinson, The heat semigroup and integrability of Lie algebras, J. Funct. Anal. 79 (2) (1988), 351-397.

64. Ola Bratteli, On some C*-dynamical systems, in Miniconferences on harmonic analysis and operator algebras, Canberra, 1987, Proc. Centre Math. Anal. Austral. Nat. Univ. 16 (Austral. Nat. Univ., Canberra, 1988), 4-7.

65. Charles J K Batty, Ola Bratteli and Derek W Robinson, The heat semigroup, derivations, and Reynolds's identity, in Operator algebras and applications 2, London Math. Soc. Lecture Note Ser. 136 (Cambridge Univ. Press, Cambridge, 1988), 23-47.

66. Ola Bratteli, Book Review: Semigroups of linear operators and applications, Bull. Amer. Math. Soc. (N.S.) 18 (1) (1988), 100-103.

67. Ola Bratteli, Fred Goodman, Palle Jorgensen and Derek W Robinson, Unitary representations of Lie groups and Gîrding's inequality, Proc. Amer. Math. Soc. 107 (3) (1989), 627-632.

68. Ola Bratteli, George A Elliott, David E Evans and Akitaka Kishimoto, Quasi-product actions of a compact abelian group on a C*-algebra, Tohoku Math. J. (2) 41 (1) (1989), 133-161.

69. Ola Bratteli and Palle E T Jorgensen, Conservative derivations and dissipative Laplacians, J. Funct. Anal. 82 (2) (1989), 404-411.

70. Ola Bratteli, George A Elliott, F M Goodman and Palle E T Jorgensen, Smooth Lie group actions on noncommutative tori, Nonlinearity 2 (2) (1989), 271-286.

71. Ola Bratteli, George A Elliott, F M Goodman and Palle E T Jorgensen, On Lie algebras of operators, J. Funct. Anal. 86 (2) (1989), 341-359.

72. Ola Bratteli, Hideki Kurose and Derek W Robinson, Comparison of commuting one-parameter groups of isometries, Trans. Amer. Math. Soc. 320 (2) (1990), 677-694.

73. Ola Bratteli and Derek W Robinson, Second-order elliptic operators and heat kernels on Lie groups, Trans. Amer. Math. Soc. 325 (2) (1991), 683-713.

74. Ola Bratteli, George A Elliott, David E Evans and Akitaka Kishimoto, Noncommutative spheres. I, Internat. J. Math. 2 (2) (1991), 139-166.

75. Ola Bratteli, George A Elliott, David E Evans and Akitaka Kishimoto, On the classification of inductive limits of inner actions of a compact group, in Current topics in operator algebras, Nara 1990 (World Sci. Publ., River Edge, NJ, 1991), 13-24.

76. Bruce Blackadar, Ola Bratteli, George A Elliott and Alexander Kumjian, Reduction of real rank in inductive limits of C*-algebras, Math. Ann. 292 (1) (1992), 111-126.

77. Ola Bratteli and Akitaka Kishimoto, Noncommutative spheres. III. Irrational rotations, Comm. Math. Phys. 147 (3) (1992), 605-624.

78. Ola Bratteli and George A Elliott, An introduction to fractal C*-algebras, in Operator algebras and topology, Craiova, 1989, Pitman Res. Notes Math. Ser. 270 (Longman Sci. Tech., Harlow, 1992), 1-29.

79. Ola Bratteli, George A Elliott, David E Evans and Akitaka Kishimoto, Noncommutative spheres. II. Rational rotations, J. Operator Theory 27 (1) (1992), 53-85.

80. Ola Bratteli, George A Elliott and Akitaka Kishimoto, Quasi-product actions of a compact group on a C*-algebra, J. Funct. Anal. 115 (2) (1993), 313-343.

81. Ola Bratteli, David E Evans and Akitaka Kishimoto, Crossed products of totally disconnected spaces by Z2 * Z2 , Ergodic Theory Dynam. Systems 13 (3) (1993), 445-484.

82. Ola Bratteli, Erling Størmer, Akitaka Kishimoto and Mikael Rørdam, The crossed product of a UHF algebra by a shift, Ergodic Theory Dynam. Systems 13 (4) (1993), 615-626.

83. Ola Bratteli (with David E Evans and Akitaka Kishimoto), The crossed product of the irrational rotation algebra by the flip, in Res. Notes Math., 5, Operator algebras, mathematical physics, and low-dimensional topology, Istanbul, 1991 (A K Peters, Wellesley, MA, 1993), 61-76.

84. Ola Bratteli, David E Evans and Akitaka Kishimoto, Almost shift invariant projections in infinite tensor products, in Quantum and non-commutative analysis, Kyoto, 1992, Math. Phys. Stud. 16 (Kluwer Acad. Publ., Dordrecht, 1993), 427-434.

85. Ola Bratteli, George A Elliott, David E Evans and Akitaka Kishimoto, Finite group actions on AF algebras obtained by folding the interval, K-Theory 8 (5) (1994), 443-464.

86. Ola Bratteli, David E Evans and Akitaka Kishimoto, The Rohlin property for quasi-free automorphisms of the fermion algebra, Proc. London Math. Soc. (3) 71 (3) (1995), 675-694.

87. Charles J K Batty, Ola Bratteli, Palle E T Jorgensen and Derek W Robinson, Asymptotics of periodic subelliptic operators, J. Geom. Anal. 5 (4) (1995), 427-443.

88. Ola Bratteli and Derek W Robinson, Subelliptic operators on Lie groups: variable coefficients, Acta Appl. Math. 42 (1) (1996), 104 pages.

89. Ola Bratteli, Palle E T Jorgensen and Geoffrey L Price, Endomorphisms of B(H), in Quantization, nonlinear partial differential equations, and operator algebra, Cambridge, MA, 1994, Proc. Sympos. Pure Math. 59 (Amer. Math. Soc., Providence, RI, 1996), 93-138.

90. Ola Bratteli and George A Elliott, Small eigenvalue variation and real rank zero, Pacific J. Math. 175 (1) (1996), 47-59.

91. Ola Bratteli and Derek W Robinson, Operator algebras and quantum statistical mechanics. 2. Equilibrium states. Models in quantum statistical mechanics (Second edition), Texts and Monographs in Physics (Springer-Verlag, Berlin, 1997).

92. Ola Bratteli and Palle E T Jorgensen, Endomorphisms of B(H) II, Finitely correlated states on O_n, J. Funct. Anal. 145 (2) (1997), 323-373.

93. Ola Bratteli and Palle E T Jorgensen, Isometries, shifts, Cuntz algebras and multiresolution wavelet analysis of scale N, Integral Equations Operator Theory 28 (4) (1997), 382-443.

94. Ola Bratteli, Akitaka Kishimoto and Derek W Robinson, Abundance of invariant and almost invariant pure states of C*-dynamical systems, Comm. Math. Phys. 187 (1997), no. 3, 491-507.

95. Ola Bratteli and Palle E T Jorgensen, A connection between multiresolution wavelet theory of scale N and representations of the Cuntz algebra $O_{N}$, in Operator algebras and quantum field theory, Rome, 1996 (Int. Press, Cambridge, MA, 1997), 151-163.

96. Ola Bratteli, George A Elliott, David E Evans and Akitaka Kishimoto, On the classification of C*-algebras of real rank zero. III. The infinite case, in Operator algebras and their applications, II, Waterloo, ON, 1994/1995, Fields Inst. Commun. 20 (Amer. Math. Soc., Providence, RI, 1998), 11-72.

97. Ola Bratteli, George A Elliott, David E Evans and Akitaka Kishimoto, Homotopy of a pair of approximately commuting unitaries in a simple C*-algebra, J. Funct. Anal. 160 (2) (1998), 466-523.

98. Ola Bratteli and Palle E T Jorgensen, Iterated function systems and permutation representations of the Cuntz algebra, Mem. Amer. Math. Soc. 139 (663) (1999), 89 pages.

99. Ola Bratteli, Palle E T Jorgensen and Derek W Robinson, Spectral asymptotics of periodic elliptic operators, Math. Z. 232 (4) (1999), 621-650.

100. Ola Bratteli and Palle E T Jorgensen, Convergence of the cascade algorithm at irregular scaling functions, in The functional and harmonic analysis of wavelets and frames, San Antonio, TX, 1999 (Contemp. Math., 247, Amer. Math. Soc., Providence, RI, 1999), 93-130.

101. Ola Bratteli, Palle E T Jorgensen, Akitaka Kishimoto and R F Werner, Pure states on $O_{d}$, J. Operator Theory 43 (1) (2000), 97-143.

102. Ola Bratteli, David E Evans and Palle E T Jorgensen, Compactly supported wavelets and representations of the Cuntz relations, Appl. Comput. Harmon. Anal. 8 (2) (2000), 166-196.

103. Ola Bratteli and Akitaka Kishimoto, Homogeneity of the pure state space of the Cuntz algebra, J. Funct. Anal. 171 (2) (2000), 331-345.

104. Ola Bratteli and Akitaka Kishimoto, Trace scaling automorphisms of certain stable AF algebras. II, Quart. J. Math. 51 (2) (2000), 131-154.

105. Ola Bratteli, Palle E T Jorgensen, Ki Hang Kim and Fred Roush, Non-stationarity of isomorphism between AF algebras defined by stationary Bratteli diagrams, Ergodic Theory Dynam. Systems 20 (6) (2000), 1639-1656.

106. Ola Bratteli, Palle E T Jorgensen, Ki Hang Kim and Fred Roush, Decidability of the isomorphism problem for stationary AF-algebras and the associated ordered simple dimension groups, Ergodic Theory Dynam. Systems 21 (6) (2001), 1625-1655.

107. Ola Bratteli and Akitaka Kishimoto, AF flows and continuous symmetries, Rev. Math. Phys. 13 (12) (2001), 1505-1528.

108. Ola Bratteli and Palle E T Jorgensen, Wavelet filters and infinite-dimensional unitary groups, in Wavelet analysis and applications, Guangzhou, 1999, AMS/IP Stud. Adv. Math. 25 (Amer. Math. Soc., Providence, RI, 2002), 35-65.

109. Ola Bratteli, Palle E T Jorgensen, Ki Hang Kim and Fred Roush, Computation of isomorphism invariants for stationary dimension groups, Ergodic Theory Dynam. Systems 22 (1) (2002), 99-127.

110. Ola Bratteli, Palle E T Jorgensen, Ki Hang Kim and Fred Roush, Corrigendum to the paper: "Decidability of the isomorphism problem for stationary AF-algebras and the associated ordered simple dimension groups'' [Ergodic Theory Dynam. Systems 21 (6) (2001), 1625-1655], Ergodic Theory Dynam. Systems 22 (2) (2002), 633.

111. Ola Bratteli, Palle E T Jorgensen, Wavelets through a looking glass. The world of the spectrum. Applied and Numerical Harmonic Analysis (Birkhauser Boston, Inc., Boston, MA ,2002).

112. Ola Bratteli, Palle E T Jorgensen and Vasyl' Ostrovs'kyi, Representation theory and numerical AF-invariants. The representations and centralizers of certain states on O_d, Mem. Amer. Math. Soc. 168 (797) (2004), 178 pages.

113. Ola Bratteli, Akitaka Kishimoto and Derek W Robinson, Rohlin flows on the Cuntz algebra $O_{\infty }$, J. Funct. Anal. 248 (2) (2007), 472-511.

114. Ola Bratteli, Akitaka Kishimoto and Derek W Robinson, Approximately inner derivations, Math. Scand. 103 (1) (2008), 141-160.

Last Updated January 2019