On isometric dilations of commutative systems of linear operators

Автор(и)

  • V. A. Zolotarev Department of Mechanics and Mathematics, V.N. Karazin Kharkov National University, 4 Svobody Sq., Kharkov, 61077, Ukraine

Ключові слова:

dilation, commutative systems of linear operators

Анотація

The isometric dilation of two parameter semigroup $T(n)=T^{n_1}_1 T^{n_2}_2$, where $n=(n_1,n_2)\in \mathbb{Z}^2_+$, for a commutative system $\{T_1,T_2\}$ of linear bounded operators, one of which is a contraction, $||T_1||\le 1$, is constructed. The building of the dilation is based on characteristic qualities of the commutative isometric expansion $\left\{V_s,\stackrel{+}{V_s}\right\}_{s=1}^2$, which was given in the previous work by the author [8]. The isometric dilations $U(n)$ and $\stackrel{+}{U}\!\!(n)$ of the semigroups $T(n)$ and $T^*(n)$ are shown to be unitarily linked.

Mathematical Subject Classification: 47A45.

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Як цитувати

(1)
Zolotarev, V. A. On isometric dilations of commutative systems of linear operators. Журн. мат. фіз. анал. геом. 2005, 1, 192-208.

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