Abstract:
The paper describes the biography and the main scientific achievements of Professor Anatolij Nikolaevich Sherstnev.
The scientific interests of A.N. Sherstnev are associated with probabilistic metric and
normed spaces, as well as with the non-commutative theory of measure and integral. He was
the first to suggest that bilinear forms should be used for solving important problems of the general theory of measure on projectors of von Neumann algebras. The fruitful ideas allowed him
and his followers to advance the general theory of non-commutative integration in operator
algebras in various directions. In particular, the scales of $L_p$-spaces of integrable bilinear forms
were constructed, the theory of conditional expectation in the indicated spaces was developed,
possibility of generalizations of the main constructions to the case of Jordan algebras was
investigated. Furthermore, some important problems in construction of unbounded measures
on projectors of von Neumann algebras were solved.
A.N. Sherstnev published over 100 research works, including the well-known monographs
and textbooks. In 1974, he organized the interuniversity scientific seminar “Operator Algebras
and Applications”. In 1973–1998, he was the head of the Department of Mathematical Analysis
at Kazan State University.
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