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This article is cited in 4 scientific papers (total in 4 papers)
On a class of unconditional bases in Hilbert spaces and on the problem of similarity of dissipative Volterra operators
G. M. Gubreev
Abstract:
Let $B$ be a completely nonselfadjoint dissipative Volterra operator acting in a separable Hilbert space $\mathfrak Y$ whose resolvent $(I-\lambda B)^{-1}$ has finite exponential type. Further, let $\mathfrak{L}=(B-B^*)\mathfrak Y$, $y\in\mathfrak{L}$, and
$y(\lambda)=(I-\lambda B)^{-1}y$. In this article conditions are determined on the operator $B$, the vector $y$, and the sequence $\Lambda=\{\lambda_k\}_{-\infty}^{+\infty}$ under which the family
$$
\{y(\lambda_k):\lambda_k\in \Lambda\}, \qquad
\inf_{\lambda_k}\operatorname{Im}\lambda_k>0,
$$
forms an unconditional basis in the space $\mathfrak Y$. Moreover, a new approach is considered for the problem of similarity of dissipative Volterra operators, based on a study of the basis properties of this system of vectors.
Received: 09.07.1990
Citation:
G. M. Gubreev, “On a class of unconditional bases in Hilbert spaces and on the problem of similarity of dissipative Volterra operators”, Mat. Sb., 183:9 (1992), 105–146; Russian Acad. Sci. Sb. Math., 77:1 (1994), 93–126
Linking options:
https://www.mathnet.ru/eng/sm1074https://doi.org/10.1070/SM1994v077n01ABEH003431 https://www.mathnet.ru/eng/sm/v183/i9/p105
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Abstract page: | 398 | Russian version PDF: | 139 | English version PDF: | 4 | References: | 53 | First page: | 1 |
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