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Matematicheskaya Fizika, Analiz, Geometriya [Mathematical Physics, Analysis, Geometry], 2004, Volume 11, Number 3, Pages 282–301
(Mi jmag208)
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This article is cited in 5 scientific papers (total in 5 papers)
Isometric expansions of commutative systems of linear operators
V. A. Zolotarev V. N. Karazin Kharkiv National University, Faculty of Mathematics and Mechanics
Abstract:
The commutative isometric expansion $\bigl\{V_s,\stackrel{+}{V_s}\bigr\}_{s=1}^2$ for a commutative system $\left\{T_1,T_2\right\}$ of linear bounded operators in Hilbert space $H$ is constructed. Building of the isometric dilation for two parameter semigroup $T(n)=T_1^{n_1}T_2^{n_2}$, where $n=(n_1;n_2)$, is based on characteristic qualities of given commutative isometric expansion. Main properties of a characteristic function $S(z)$, corresponding to the commutative isometric expansion $\bigl\{V_s,\stackrel{+}{V_s}\bigr\}_{s=1}^2$ are described. An analogue of Hamilton–Cayley theorem is proved. It is shown that there exists polynomial $\mathbb{P}(z_1,z_2)$ such as $\mathbb{P}(T_1,T_2)=0$ when the defect subspaces of system $\{T_1,T_2\}$ are of finite dimension.
Received: 10.11.2003
Citation:
V. A. Zolotarev, “Isometric expansions of commutative systems of linear operators”, Mat. Fiz. Anal. Geom., 11:3 (2004), 282–301
Linking options:
https://www.mathnet.ru/eng/jmag208 https://www.mathnet.ru/eng/jmag/v11/i3/p282
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