(1907–1989), Soviet mathematician. The son of a Kievan lumber merchant, Mark Krein showed an early talent for mathematics, attending research seminars at age 14. While he never obtained an undergraduate degree, he was accepted for doctoral studies at Odessa University in 1926, completing them in 1929. He became the author of more than 300 papers and monographs that opened up new areas of mathematics and greatly enriched the more traditional ones. Krein’s work was characterized by a profound intrinsic unity and a close interlacing of general abstract and geometric ideas with concrete and analytical results and applications.
An excellent and enthusiastic teacher, Krein attracted many students. In the 1930s he created an important center of functional analysis at Odessa University. His interests included geometry of Banach spaces, moment problems, integral equations and matrices, spectral theory of linear operators, extension problems and applications. Many of his results from this period, as well as joint results with colleagues and students, are considered classic and appear in all textbooks of functional analysis. In 1939 Krein was elected corresponding member of the Ukrainian Academy of Sciences.
Evacuated during World War II, he became chair of theoretical mechanics at Kuibyshev Industrial Institute. In 1944 he returned to Odessa but was soon dismissed from the university. This was the end of the famous center of functional analysis at Odessa University. From 1944 to 1952 Krein held a part-time position as head of the department of functional analysis and algebra at the Mathematical Institute of the Ukrainian Academy of Sciences in Kiev. But he lost this post in 1952, ostensibly because he was not a permanent resident of Kiev. Both dismissals were engineered by professional and administrative rivals who, taking advantage of officially supported antisemitism in Ukraine and especially Odessa, accused him of Jewish nationalism on the grounds that too many of his prewar students had been Jews. This accusation was included in his classified file and was held against him all his life. From 1944 to 1954 he was a professor of theoretical mechanics at the Odessa Marine Engineering Institute, and from 1954 until his retirement, he held the chair of theoretical mechanics at the Odessa Civil Engineering Institute. In his last years he was a consultant to the Institute of Physical Chemistry of the Ukrainian Academy of Sciences in Odessa.
Once he had lost his university base, Krein was not allowed to have Jewish students. All attempts by professional societies and individuals to get him some measure of official recognition proved unsuccessful.
Krein responded to his hostile surroundings with hard work and research. He and many of his students were protected by his outstanding achievements. In retrospect, he clearly won the struggle. Not only was he able to devote his life to teaching and research in mathematics, but remaining in Odessa, the city he loved, he led a strong and dedicated group of scholars who from 1949 until his death met regularly at the Academic Club and sometimes in his home. He had a great impact on the development of mathematics and its applications throughout the world. While he was never allowed to travel abroad, his work knew no borders. In 1968 Krein was elected honorary member of the American Academy of Arts and Sciences and in 1979 foreign member of the U.S. National Academy of Sciences.
In 1982 in Jerusalem, Krein was awarded the prestigious Wolf Prize in Mathematics. According to the prize citation, “Krein brought the full force of mathematical analysis to bear on problems of function theory, operator theory, probability and mathematical physics. His contributions led to important developments in the applications of mathematics to different fields ranging from theoretical mechanics to electrical engineering. His style in mathematics and his personal leadership and integrity have set standards of excellence.”
V. M. Adamian, Israel Gohberg, Miroslav L’vovich Gorbachuk, Valentina Ivanovna Gorbachuk, et al., eds., Differential Operators and Related Topics: Proceedings of the Mark Krein International Conference on Operator Theory Advances and Applications, Odessa, Ukraine, August 18–22, 1997, Operator Theory, Advances and Applications 117 (Basel and Boston, 2000), p. 420, this volume also contains the complete list of publications of M. G. Krein; V. M. Adamian, Israel Gohberg, Miroslav L’vovich Gorbachuk, Valentina Ivanovna Gorbachuk, et al., eds., Operator Theory and Related Topics: Proceedings of the Mark Krein Inter-national Conference on Operator Theory Advances and Applications, Odessa, Ukraine, August 18–22, 1997, Operator Theory, Advances and Applications 118 (Basel and Boston, 2000), p. 419; Israel Gohberg and Mark Kac, eds., Topics in Functional Analysis: Essays Dedicated to M. G. Krein on the Occasion of His 70th Birthday, Advances in Mathematics: Supplementary Studies 3 (New York, 1978), p. 395; Integral Equations and Operator Theory 30.2–4 and 31.1 (1998), special memorial issues commemorating the ninetieth anniversary of the birth of M. G. Krein.