**Mikhail Kadets** was a Ukranian mathematician who worked in analysis and the theory of Banach spaces.

- Iosiph Mikhailovich was arrested in 1937, the year that the 'Great Terror' was at its worst, and declared to be one of the 'Enemies of the People'.
- The Molotov-Ribbentrop non-aggression pact between Germany and the Soviet Union meant that the initial years of the war had little effect on life in Kharkov and Kadets continued his secondary school education.
- This occurred only a few days after Kadets graduated from secondary school.
- German troops advanced towards Kharkov and Kadets was evacuated from the city and underwent military training.
- In 1946 Kadets enrolled in the Faculty of Physics and Mathematics of Kharkov State University.
- 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.
- In 1948 a Ukrainian translation was published and Kadets began to study the book.
- Of course the book presented many powerful methods which Kadets found very useful but it was the problems that Banach posed in this work which provided the most fascination.
- Banach's problems were a constant challenge to Kadets throughout his life and they inspired much of his mathematical output.
- In some ways one might consider Banach as Kadets' supervisor, not of course in any personal sense because Banach died before Kadets began his university studies, but rather through the inspiration and guidance that his book provided.
- Although Levin didn't suggest research problems for Kadets to work on, nevertheless, it was Levin who provided him with good advice and was a strong influence on him.
- Many students do some teaching but this was not the case for Kadets who concentrated on research.
- After completing his first degree in 1950, Kadets went to Makeevka in the Donetsk region where he was employed as a research assistant in the Scientific Research Institute of the Ministry of Coal Mining.
- One of the departments of the Institute of Coal Mining was 'Fire-fighting technology' and Kadets taught mathematics and physics in this department.
- The problem that Kadets worked on for his Ph.D. was the Fréchet-Banach problem on the topological equivalence of all separable infinite-dimensional Banach spaces.
- Kadets was able to solve a special case of the Fréchet-Banach problem in his first publication which appeared in 1953.
- 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.
- Having been awarded his Ph.D. in 1955, Kadets remained working at the Ministry of Coal Mining in Makeevka for another two years.
- Today this important result is often known as 'Kadets Theorem'.
- This result brought Kadets international fame and he was invited to the Symposium on Infinite Dimensional Topology to be held at Louisiana State University in Baton Rouge in the United States in March 1967.
- Kadets applied to be allowed to travel to the symposium but, as was usual, his application was refused.
- We choose not to describe the long list of highly significant results on Banach spaces that Kadets proved throughout his career but we refer the reader to the articles in the references where a good overview of these important contributions is given.
- From 1965, Kadets worked at the Kharkov State Academy of Municipal Economy as well as at Kharkov University where he gave courses on Functional Analysis and, in particular, high powered courses on Banach spaces such as 'Series in Banach spaces', 'Biorthogonal systems and bases', 'Theory of renormings' and similar specialist topics related to his research interests.
- We give information about Vladimir Mikhailovich Kadets' career below.
- In particular, a result of V M Kadets states that every infinite-dimensional space contains series with nonconvex sum-set.
- Mikhail Iosifovich Kadets was a brilliant and an exceptionally deep mathematician, a kind and sympathetic person, witty and pleasant to talk with.
- He continued to undertake research at Rostov-on-Don State University with Naum Samoilovich Landkof (born 1915), who had been a student of Mikhail Alekseevich Lavrent'ev, as his thesis advisor.

Born 30 November 1923, Kiev, Soviet Empire (now Kyiv, Ukraine). Died 7 March 2011, Kharkov, Ukraine.

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Origin Ukraine, Topology

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive