Ukrainian Mathematical Bulletin

Volume 1, Issue 4, 2004 pp. 537-552.

Theory of Operators and Involution Representations of Algebras

Authors: Yurii S. Samoilenko and Maxim V. Zavodovsky
Author institution: Institute of Mathematics,National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka Str. 01601, Kyiv-4, Ukraine

Summary: In this paper, we make a review of the results obtained in the Department of Functional Analysis in the Institute of Mathematics of the National Academy of Sciences of Ukraine. The results are obtained on a description of the structure of algebras that have their generators satisfying a linear relation and a given spectrum. We also study $*$-re\-presentations of these algebras and consider their applications.

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