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Mark Aronovich Naimark

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5 Dec 1909

Odessa, Ukraine

30 Dec 1978

Moscow, USSR

Mark Naimark studied mathematics on his own for four years from the age of fifteen completing a university course on analysis. He entered the Odessa Institute of National Education in 1929. Then, in 1933, he went to Odessa State University to undertake graduate studies.

Naimark defended his candidate's dissertation in 1936 the moved to the University of Moscow in 1938. In 1941 he received his doctorate from the Steklov Mathematical Institute of the USSR Academy of Sciences . He was appointed to a chair at the Seismological Institute of the USSR Academy of Sciences .

During World War II he undertook military work in a number of different places, returning to Moscow at the end of the War. In 1954 he was appointed professor at the Moscow Physical-Technical Institute. Then in 1962 he became professor at the Steklov Mathematical Institute, a post he remained in until his death.

Naimark's first work for his candidate's thesis was on the separation of roots of algebraic equations. Once he had established himself in Moscow he worked on functional analysis and group representations .

In 1943 he proved the Gelfand -Naimark theorem on self-adjoint algebras of operators in Hilbert space . In the same year he generalised von Neumann 's spectral theorem to locally compact abelian groups .

He made a detailed analysis of the infinite-dimensional representations of the semisimple Lie groups . His important treatise with Gelfand on irreducible representations of the classical matrix groups was published in 1950. This work formed the basis for later work by Harish-Chandra on representations of semisimple Lie groups.

Naimark also contributed to Banach spaces. He wrote the famous text Normed Rings in 1956. He had written the book Linear differential operators two years earlier in 1954.

In all Naimark wrote 123 papers and 5 books. His last book was Theory of group representations published in 1976. By the time this book was written Naimark was suffering from heart disease. Too ill to sit up, he dictated the text to his wife.

Source:School of Mathematics and Statistics University of St Andrews, Scotland