Mychajlo Kadez

Mykhaylo Jossypowytsch Kadez ( Ukrainian Михайло Йосипович Кадець , Russian Михаил Иосифович Кадец Mikhail Iosifovich Kadec , in English transliteration also Mikhail Iosiphovich Kadets * thirtieth November 1923 in Kiev , Ukrainian SSR , † 7. March 2011 in Kharkiv , Ukraine ) was a Soviet mathematician who dealt with analysis and Banach space theory .

life and work

Kadez was born in Kiev. In 1943 he was called up for military service. After demobilization in 1946, he studied at Kharkiv University , graduating in 1950. After a few years in Makiyivka , he returned to Kharkiv in 1957 , where he spent the rest of his life and worked at various institutes. Under Boris Lewin he received his diploma in 1955 and his doctorate in 1963. In 2005 he was awarded the Ukrainian State Prize.

Reading a Ukrainian translation of Banach's monograph Théorie des opérations linéaires aroused his interest in Banach's space theory. In 1966 he was able to positively solve the Banach - Fréchet problem, whether two infinitely dimensional separable Banach spaces are homeomorphic as topological spaces . He developed the equivalent norms method , which found numerous applications. For example, he showed that an infinitely dimensional separable Banach space has an equivalent, Fréchet-differentiable norm if and only if the dual space is also separable.

Together with Aleksander Pełczyński he achieved important results on the topological structure of L ^p spaces .

Furthermore, Kadec made several contributions to the theory of finite-dimensional normalized spaces . Together with MI Snobar he displayed in 1971 the so-called today set of Kadec-Snobar whereby each -dimensional subspace of a normalized space, the image of a projection with standard maximum is. Together with VI Guarii and VI Matsaew found the exact value of the Banach-Mazur distance of the -dimensional spaces and . ${\displaystyle n}$ ${\displaystyle \textstyle {\sqrt {n}}}$ ${\displaystyle n}$ ${\displaystyle \ell _{p}^{n}}$ ${\displaystyle \ell _{q}^{n}}$

In the harmonic analysis in 1964 he showed the Kadec theorem, which is now called the -theorem, that if a sequence is with , the function sequence is a Riesz basis in L ² [-π, π] . ${\displaystyle {\tfrac {1}{4}}}$ ${\displaystyle (\lambda _{n})}$ ${\displaystyle \sup |\lambda _{n}-n|<{\tfrac {1}{4}}}$ ${\displaystyle x\mapsto \exp(\mathrm {i} \lambda _{n}x)}$

Kadez is considered to be the founder of the Kharkiv school for Banach spaces. Together with his son Vladimir M. Kadec, he wrote two books about rows in Banach rooms.

Web links

• John J. O'Connor, Edmund F. Robertson :  Mychajlo Kadez. In: MacTutor History of Mathematics archive .

Individual evidence

1. ↑ In memory of Mikhail Iosifovich Kadets (1923–2011) , Zh. Mat. Fiz. Anal. Geom. Volume 7.2 (2011), pages 194-195
2. ^ Yurii I. Lyubich, Vladimir A. Marchenko, Sergei P. Novikov, MI Ostrovskii, Leonid A. Pastur, Anatolii N. Plichko, MM Popov, Evgenii M. Semenov, SL Troyanskii, Vladimir P. Fonf, Evgenii Ya. Khruslov: Mikhail Iosifovich Kadets (obituary) , Russian Math. Surveys, Vol. 66.4 (2011), 809
3. ↑ IM Gelfand, last2 = B. Ya Levin, VA Marchenko, AV Pogorelov, SL Sobolev: Mikhail Iosifovich Kadets (on the occasion of his sixth birthday) , Russian Math. Surveys, vol. 39,6 (1984), pages 231-232
4. ↑ Mikhail Iosifovich Kadets in the Mathematics Genealogy Project (English)
5. ↑ Mikhail Iosiphovich Kadets 1923-2011 (Russian and English)
6. ↑ MI Ostrovskii, AM Plichko: On the Ukrainian translation of “Théorie des opérations linéaires” and Mazur's updates of the “remarks” section , Mat. Stud., Volume 32, 1 (2009), pages 96-111
7. ^ ^{A b} Albrecht Pietsch: History of Banach spaces and linear operators , Birkhäuser Boston, Inc. 2007, ISBN 978-0-8176-4367-6 , page 609
8. ↑ Bernard Beauzamy: Introduction to Banach spaces and Their geometry , North-Holland Mathematics Studies, Volume 68 (1985), ISBN 0-444-87878-5 , Chapter VI
9. ^ R. Meise, D. Vogt: Introduction to functional analysis . Vieweg, 1992, ISBN 3-528-07262-8 , sentence 12.14
10. ^ Nicole Tomczak-Jaegermann: Banach-Mazur distances and finite-dimensional operator ideals , Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific & Technical, Volume 38 (1989), ISBN 0-582-01374-7 , page 138
11. ^ John Rowland Higgins: Completeness and basis properties of sets of special functions , Cambridge University Press 1977, Cambridge Tracts in Mathematics, Volume 72, ISBN 0-521-21376-2
12. ↑ MI Kadets, VM Kadets: Series in Banach spaces: Conditional and unconditional convergence , Birkhäuser Verlag 1997, Operator Theory: Advances and Applications, Volume 94, ISBN 3-7643-5401-1