Mikhail Iosiphovich Kadets (russian: Михаил Иосифович Кадец, uk, Михайло Йосипович Кадець , sometimes transliterated as Kadec, 30 November 1923 – 7 March 2011) was a Soviet-born Jewish mathematician working in
analysis
Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...
and the theory of
Banach spaces.
Life and work
Kadets was born in Kiev. In 1943, he was drafted into the army. After demobilisation in 1946, he studied at
Kharkov University
The Kharkiv University or Karazin University ( uk, Каразінський університет), or officially V. N. Karazin Kharkiv National University ( uk, Харківський національний університет імені ...
, graduating in 1950. After several years in
Makeevka he returned to Kharkov in 1957, where he spent the remainder of his life working at various institutes. He defended his PhD in 1955 (under the supervision of
Boris Levin
Boris Yakovlevich Levin ( rus, Борис Яковлевич Левин, 22 December 1906 – 24 August 1993) was a Soviet mathematician who made significant contributions to complex analysis, function theory.
Biography
Boris Yakovlevich Levin ...
), and his doctoral dissertation in 1963. He was awarded the State Prize of Ukraine in 2005.
After reading the Ukrainian translation of
Banach's monograph ''
Théorie des Opérations Linéaires'', he became interested in the theory of Banach spaces. In 1966, Kadets solved in the affirmative the
Banach–
Fréchet problem, asking whether every two
separable infinite-dimensional Banach spaces are
homeomorphic. He developed the method of equivalent norms, which has found numerous applications. For example, he showed that every separable Banach space admits an equivalent
Fréchet differentiable norm if and only if the
dual space is separable.
Together with
Aleksander Pełczyński
Aleksander "Olek" Pełczyński (2 July 1932, Tarnopol, Poland – 20 December 2012, Wrocław) was a Polish mathematician who worked in functional analysis.
Career
Pełczyński studied mathematics from 1950 to 1956 at the University of Warsaw an ...
, he obtained important results on the topological structure of
Lp spaces.
Kadets also made several contributions to the theory of finite-dimensional normed spaces. Together with M. G. Snobar (1971), he showed that every
-dimensional subspace of a Banach space is the image of a projection of norm at most
Together with
V. I. Gurarii and V. I. Matsaev, he found the exact order of magnitude of the
Banach–Mazur distance between the
-dimensional spaces
and
In
harmonic analysis, Kadets proved (1964) what is now called the Kadets
theorem, which states that, if
for all integers
then the sequence
is a
Riesz basis in