Both were excellent lecturers. Baltaga, who gave the course on mathematical analysis, drew Kadets' attention to the question of infinite-dimensional extensions of the theorem of Steinitz on conditionally convergent series. Later this became one of the directions of Kadets' scientific activity. Kadets attended Levin's special courses on "Almost periodic functions" and "Banach spaces", which played an important part in determining his scientific interests.

To the solution of the problem he applied arguments of approximation theory suggested by Bernstein's theorem on the recovery of a continuous function from its least deviations from polynomials. Since the best approximations in a normed space behave the more regularly the "more convex" the norm of this space is, an essential part of the method is the introduction in the given space of an equivalent norm having sufficiently good properties. The combination of the technique of best approximations with the technique of equivalent norms enabled Kadets to prove the homeomorphic property successively in still wider classes: uniformly convex, reflexive, conjugate.

We send you greetings from the Symposium on Infinite Dimensional Topology and we express our regrets that you were unable to join us.

... a disciplined, keen, and concise language on a background of meticulous techniques of analysis and geometry.

... the spouse of the senior and the mother of the junior of the authors, who took upon herself the worries of everyday life - without the freedom she thus provided we would never have decided to undertake the work whose results are now offered to the reader.

The central theme of this book stems from a theorem of E Steinitz dating from 1913. The "sum-set" of a series will mean the set of all sums of convergent rearrangements of the series. Steinitz's theorem says that if $\sum x_{n}$ is a convergent series in a finite-dimensional Banach space X, with sum s, then its sum-set is a linear subset of X ... An example of Marcinkiewicz (wrongly recorded in the "Scottish book" and later reconstructed by Kornilov) showed that in infinite-dimensional spaces the sum-set need not be convex. The book under review gives a full account of later developments related to this theorem; some are quite recent, and several are the work of the authors themselves. In particular, a result of V M Kadets states that every infinite-dimensional space contains series with nonconvex sum-set. ... The book also includes some of the theory of unconditionally convergent series (for which, of course, rearrangement introduces no new points). This part of the material is more standard and largely covered in other books. ... A wealth of supplementary information is gathered in the form of exercises (some far from trivial, but hints are given), and the book concludes with a survey of unsolved problems.

Series of scalars, vectors, or functions are among the fundamental objects of mathematical analysis. When the arrangement of the terms is fixed, investigating a series amounts to investigating the sequence of its partial sums. In this case the theory of series is a part of the theory of sequences, which deals with their convergence, asymptotic behaviour etc. The specific character of the theory of series manifests itself when one considers rearrangements (permutations) of the terms of a series, which brings combinatorial considerations into the problem studied. The phenomenon that a numerical series can change its sum when the order of its terms is changed is one of the most impressive facts encountered in a university analysis course. The present book is devoted precisely to this aspect of the theory of series whose terms are elements of Banach (as well as other topological linear) spaces. The exposition focuses on two complementary problems. The first is to characterise those series in a given space that remain convergent (and have the same sum) for any rearrangement of their terms; such series are usually called unconditionally convergent. The second problem is, when a series converges only for certain rearrangements of its terms (in other words, converges conditionally), to describe its sum range, i.e. the set of sums of all its convergent rearrangements.

A new chapter devoted to non-norm topologies presents the authors' results showing that a sum range can be non-convex for the weak topology and for convergence in measure, and the theorem of Banaszczyk stating that the Steinitz property holds in nuclear metrizable spaces. Finally, a 20-page appendix describes recent work by the authors on the set of limits of Riemann sums I(f) of a vector-valued function f on a real interval, showing close analogies with the earlier results of sum ranges.

Kadets devoted much time and effort to his pedagogical activities. Nineteen of his students defended their Ph.D. dissertations and among them seven became doctors of the sciences. He was generous in sharing his mathematical ideas with his students. His Kharkov school was well known internationally. ... Mikhail Iosifovich Kadets was a brilliant and an exceptionally deep mathematician, a kind and sympathetic person, witty and pleasant to talk with. That is how he will remain in our thoughts.

All who know Kadets esteem highly his independent character and the great demands he makes on himself, the breadth of his scientific interests and his sense of humour.