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Tokyo Journal of Mathematics

Sakhnovich — Biography Abstract. His parents worked at the coach construction factory.

In almost all of the former inhabitants of this colony that moved to the cities were arrested under various false accusations. Aron Sakhnovich was arrested on January It happened at night when Lev was asleep, but the father woke him up to bid him farewell. Although the hypocrites from the NKVD tried to stop Aron Sakhnovich from saying good-bye to his son telling him that he would be back soon, he knew better. In the family tried to find out what had happened to Aron Isakovich. Finally, at the end of the 80s the family was informed that Aron Sakhnovich was shot in April and was posthumously exculpated.

Gohberg and L.

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Sakhnovich eds. The Vladimir Petrovich Potapov memorial volume. Theory Adv. In the summer of , I finally finished school. Then I failed the admission exams at the University of Odessa. My mood was somber. In this paper we provide a study of quaternionic inner product spaces.

Characterizations of Inner Product Spaces

This includes ortho-complemented subspaces, fundamental decompositions as well as a number of results of topological nature. Our main purpose is to show that a closed uniformly positive subspace in a quaternionic Krein space is ortho-complemented, and this leads to our choice of the results presented in the paper. We study infinite products of reproducing kernels with view to their use in dynamics of iterated function systems , in harmonic analysis, and in stochastic processes.

On the way, we construct a new family of representations of the Cuntz relations. Then, using these representations we associate a fixed filled Julia set with a Hilbert space. This is based on analysis and conformal geometry of a fixed rational mapping R in one complex variable, and its iterations. Operator-valued Q -functions for special pairs of nonnegative selfadjoint extensions of nonnegative not necessarily densely defined operators are defined and their analytical properties are studied.

This paper presents a proof of the Radon—Nikodym theorem for vector measures with values in a Hilbert space or in the space of bounded linear operators acting from a Hilbert space to a Hilbert space. Assertions for these cases are known [13], [14], [15] , however they contain some mistakes and inaccuraces see Concluding Remarks at the end of this paper.

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Considering operator-valued measures, we emphasize distinctions between the uniform and strong topologies see Remark 2. There exist more general versions of the Radon—Nikodym theorem: for measures with values in Banach spaces with boundedly complete Schauder basis or for separable dual Banach spaces detailed exposition and history can be found, e. However, we think that a direct and simple proof for the Hilbert space case is of independent interest.

The matrices involved in the realizations are computed from state space realizations of the data functions G and K. On the one hand the results are based on the commutant lifting theorem and on the other hand on stabilizing solutions of algebraic Riccati equations related to spectral factorizations.

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My Content 1 Recently viewed 1 On linear operators pr Show Summary Details. More options …. Editor-in-Chief: Oniciuc, Cezar. Open Access.

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Volume 56 Issue 1 Dec , pp. Previous Article. Next Article. On linear operators preserving orthogonality. Abstract In this paper we present some relationships among Birkhoff orthogonality and other concepts in convex analysis. Export Citation This content is open access.