# Ola Bratteli

### Quick Info

Oslo, Norway

Oslo, Norway

**Ola Bratteli**was a Norwegian mathematician who worked on operator algebras and quantum statistical mechanics.

### Biography

**Ola Bratteli**was the son of Trygve Martin Bratteli (1910-1984) and Randi Helene Larssen (1924-2002). Trygve Bratteli was a construction worker and carpenter who became an active resistance worker during the Second World War and was arrested by the Germans in 1942. He was held in German concentration camps until 1945. He married the journalist Randi Helene Larssen, the daughter of the resistance workers Olav Larssen and Aslaug Rustad, on 16 April 1946. Trygve became chairman of the Defence Commission in 1946 and was elected to parliament in May 1950. He was Finance Minister from November 1951 to January 1955, and again from December 1956 to April 1960. Then he was Minister of Transport until January 1964. Ola had a sister Marianne Bratteli who was born in 1951. She became an artist who has exhibited in many galleries around the world.

Ola Bratteli joined the Framfylkingen when he was young. This was an organisation set up by the Norwegian Labour Party in 1934 to have children take part in socialist outdoor activities. The reason for the founding of the organization was, first, that adults in the labour movement did not want the children to participate in "bourgeois organisations" such as the scout movement, for they believed this would affect the children's attitudes when they grew up. Secondly, they wanted to create an organization where children could have an outdoor recreation programme as an important ingredient. Many of the children who Bratteli knew through Framfylkingen went on to become politicians but he said [5]:-

I quickly lost interest. Politics is about making a choice and getting its case through. I really do not like to decide. I'm more concerned with understanding things.He attended the Oslo Cathedral School and, after graduating, he entered the University of Oslo to study mathematics. He graduated with a cand.mag degree and continued studying at the University of Oslo for his cand.real degree (the equivalent to a Master's degree). For this degree it was necessary to write a dissertation and he was assigned Erling Størmer as his advisor. Størmer (born 1937) was a Norwegian mathematician who had studied for his Ph.D. at Columbia University in New York advised by Richard Kadison. He was awarded the degree in 1963 for his thesis

*Point Measures in the Two-Sided Non-Commutative Integration Theory.*Størmer said [4]:-

I met [Ola] for the first time when he was about to begin his postgraduate thesis. Then he was a healthy looking dark-haired boy with a beard who often went on very long skiing trips. It soon struck me that he was a very efficient person who quickly developed a new theory. He had learned a lot about the field of operator algebras, in which he wanted to work.This quotation is from a version of the talk Størmer gave at a memorial meeting for Ola Bratteli in 2015. For a version of the full talk,

*Remarks on Professor Ola Bratteli*, see THIS LINK.

Bratteli said in the 2008 interview [5]:-

My supervisor, Erling Størmer, had given me the task of studying a mathematical object of a type that had not been analysed before. I struggled a little at first, but then it went very fast. I delivered the work as a cand.real dissertation, corresponding to today's master's thesis, and did not think more about it before Erling came rushing in. "Oh, Ola, we've made a big mistake," he said. "This should have been a doctorate."Bratteli published his outstanding results in

*Inductive limits of finite dimensional C*-algebras*(1972). He gives the following acknowledgement in the paper:-

I wish to thank my supervisor Erling Størmer. Without his many helpful suggestions this work could not have been done.After the award of his cand.real degree, Bratteli went to the United States to undertake research for his Ph.D. He was advised to take this route by Størmer who had himself gone to New York for his Ph.D. One of Størmer's fellow Ph.D. students in New York had been James Gilbert Glimm (born 24 March 1934) who also had Richard Kadison as his thesis advisor. Glimm had worked on operator algebras and in fact Bratteli's cand.real dissertation was essentially a generalisation of this work of Glimm. After working at the Massachusetts Institute of Technology for eight years, Glimm had been appointed as a professor at the Courant Institute of Mathematical Sciences, part of New York University, in 1968. Størmer had advised Bratteli to study for his doctorate with Glimm in New York. Bratteli had another reason to leave Norway, namely that his father had become parliamentary leader of the Norwegian Labour Party in 1964 and then, on 17 March 1971, had become Prime Minister of Norway. Going abroad, Bratteli said, was a kind of escape since with his father being Prime Minister there was no way he could live anonymously.

In many ways his time with Glimm in New York was a great success. Bratteli published

*Conservation of estimates in quantum field theory*(1972) in which he wrote:-

I thank James Glimm for proposing the problem of this paper, and for encouragement and valuable advice during its preparation, and I thank John Dimock for carefully reading through the manuscript.He also published

*Local norm convergence of states on the zero time Bose fields*(1974) in which he gave the following acknowledgement:-

I wish to thank James Glimm for proposing this work, and for making helpful comments. This research was carried out at the Courant Institute of Mathematical Sciences, New York University, with support from Norwegian Research Council for Science and Humanities, Norway.In other ways he was less satisfied with his time in New York although his small apartment in Greenwich Village, overlooking Washington Square, was only a short distance from New York University. He said [5]:-

I wasted a lot of time on all kinds of theatre and exhibitions. It was a very nice time. Unfortunately, the quantum field theory never got a proper look in. The method we used did not work.He did not complete his Ph.D. in New York but returned to Norway after two years. Størmer was surprised at how Bratteli had changed [4]:-

In addition to his studies, Ola spent a lot of time in the cultural life in New York and eating well. During the two years his appearance changed a lot; a lot of his hair was gone, his beard had disappeared, and he had put on so much weight that when I met him a few years later, I didn't recognize him, so I introduced myself to him.Bratteli was awarded a doctorate from the University of Oslo in 1974 for his thesis

*Inductive limits of finite dimensional C*-algebras.*Still keen to work abroad, particularly since his father had become Norwegian Prime Minister for the second time in 1973, he went to the Centre de Physique Théorique in Marseille, France. This Centre was a leading place for the study of quantum physics through operator algebra and fitted precisely with his interests. It had been set up in the early 1960s, when a theoretical group was founded on the campus of Saint-Charles in the city centre of Marseille (University of Provence). A few years later, this group settled on the campus Joseph-Aiguier, and it was there when Bratteli joined them after the award of his doctorate. In 1978 the Centre de Physique Théorique moved again, this time to the campus of Luminy. It was at the Centre de Physique Théorique that Bratteli met Derek W Robinson, a British mathematician, and they became close friends and collaborators. Robinson (born 1935) had studied at the University of Oxford and was a professor in Marseille for ten years from around 1968. Speaking of the Centre de Physique Théorique, Bratteli said [5]:-

These Frenchmen always wanted to go to Paris. Marseille was not exactly an academic place, but they had a group of highly skilled mathematicians there. In fact, I spent four years together, divided into several periods. ... My French was basically a scandal, but I managed to live in everyday life. I wonder if there is anything about one's intellectual capacity being used up by logical thinking. At least I have noticed that some colleagues have the same problem.Bratteli attended the "Conference on C*-algebras and their Applications in Theoretical Physics" held in Rome from 13-18 October 1975 and published the paper

*Self-adjointness of unbounded derivations on C*-algebras*in the Proceedings of the onference. His first paper written jointly with Derek W Robinson was

*Green's functions, Hamiltonians and modular automorphisms*(1976). As well as undertaking research at the Centre de Physique Théorique in Marseille, Bratteli also spent time at the Zentrum für interdisziplinäre Forschung of Bielefeld University in Germany.

In 1978 Derek Robinson became a professor at the Australian National University. Bratteli continued to collaborate with Robinson and made several trips to Australia. On one of these trips he stopped in Thailand and met Wasana in Bangkok. They later married.

In 1980 Bratteli became a professor at the Norwegian University of Technology in Trondheim. He remained there until 1991 when he moved to Oslo to become professor at the University of Oslo. His publication record from his time in Trondheim until 2008 was remarkable. Partly it came about because every summer, and sometimes also in the Christmas holidays, he would go and visit other mathematicians and they would spend their time on research ending up with many-author papers. In fact the last single author paper Bratteli wrote was a conference paper published in 1988, and he had around 50 multi-author works in the following 20 years.

For a list of papers by Bratteli, see THIS LINK.

In 1980, in collaboration with Derek Robinson, he published

*Operator algebras and quantum statistical mechanics, Volumes I and II*. In some ways

*Bratteli considered this his greatest achievement [5]:-*

That book is one of the things I am most proud of. Not only has it become the most cited textbook on the subject, it also contains some original work. For example, the book contains an explanation of the phenomenon of magnetism, using mathematical analysis.S Sakai, in the review of this book, wrote [3]:-

In the book under review, the authors describe the elementary theory of operator algebras and parts of the up-to-date advanced theory which are of relevance to mathematical physics. Subsequently they describe various applications to statistical mechanics. The selection of topics from the advanced theory in this book is reasonable, though it somewhat leans towards the research directions and tastes of the authors. The reference list is not complete, so that references on the historical background in some sections are not enough. However these minor criticisms are negligible. By and large the authors have excellently done the difficult job of exposing the subject matter which is a mixture of standard theory and new research work which has not previously appeared in book form. It is a good textbook for mathematicians and physicists who want to learn the C*-quantum physics.Bratteli wrote several further books. For example, he co-authored

*Wavelets through a looking glass*(2002) with Palle Jorgensen. Gilbert Walter writes in a review:-

In the last few years, a plethora of books on wavelets have appeared. Most have been variations on the same themes which were covered in some detail by Daubechies in 1992 and by Meyer in 1990. So I was expecting more of the same in this book. But it's different, a lot different. One difference is its point of view which derives more from mathematical physics than from signal processing. This enables the authors to take a fresh look at the subject and develop a new intuition for many topics. It particular, they make more extensive use of spectral theory than is usual in the subject. The book also has a number of unusual aspects in its organization. Each of the six chapters begins with a relatively intuitive vignette which is written in a more leisurely style than other parts of the book. These sections give the book much of its flavour; they are entitled respectively: "Overture: why wavelets'', "The dangers of navigating the landscape of wavelets'', "The world of the spectrum'', "A slanted matrix from dynamics'', "The fine structure of correlation'', and "The other side of wavelets''. Each gives an introduction to the topics in the chapter and explains why they are discussed and where they come from.We learn something of Bratteli's character from the description of his room given by his interviewer in [5]:-

Ola Bratteli is a very modest man. Still, he lets us enter into the innermost living room, where thin curtains dim the light before it falls on art and antiques from all parts of the world. "'The four seasons' come from Shanghai," he tells me, "I liked the sensitivity of the female artist, though it is not easy to say what that season is like. The abstract image over there I bought from a local artist when I lived in Marseille. Marianne, my youngest sister, who is a painter, cannot endure it." The Möbius Award from the Research Council of Norway, which Ola Bratteli and Erling Størmer shared in 2004 for outstanding research in the field of operator algebra, fights for one's attention with Russian jewelry boxes and Thai Buddha figures. I ask him about the bust in the corner. "It is my father, Nils Aas made it," he tells me, "I inherited it when Mom died. Father was prime minister in the seventies, yes, but you might know that?"Bratteli received several awards for his outstanding research. For example, he received: (i) The Professor Ingerid Dal and Sister Ulrikke Greve Dal's scholarship in support of humanistic research in 2001; (ii) The Nansen Foundation's prize for outstanding research from The Norwegian Academy of Sciences in 2004; and (iii) The Research Council of Norway's prize, the Möbius Prize, for outstanding research in 2004. This last mentioned prize he shared with Erling Størmer.

### References (show)

- T Digernes , E Størmer and C F Skau, Nekrolog: Ola Bratteli,
*Aftenposten*(12 February 2015). https://www.aftenposten.no/personalia/i/xRVy8/Nekrolog-Ola-Bratteli - L Lindstrøm, Ola Bratteli,
*Store norske leksikon*(3 March 2015), https://snl.no/Ola_Bratteli - S Sakai, Review: Operator algebras and quantum statistical mechanics, Volumes I and II, by Ola Bratelli and Derek W Robinson,
*Bull. Amer. Math. Soc.***7**(2) (1982), 425-427. - E Størmer, Minnetale over Professor Ola Bratteli holdt på møte 11. juni 2015. https://docplayer.me/24716764-Minnetale-over-professor-ola-bratteli-holdt-pa-mote-11-juni-av-professor-erling-stormer.html
- K Tveito, Statsministerens sønn,
*Apollon*(2008). https://www.apollon.uio.no/portretter/2008/bratteli.html

### Additional Resources (show)

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Written by J J O'Connor and E F Robertson

Last Update January 2019

Last Update January 2019