Estimates for resolvents and functions of operator pencils on tensor products of Hilbert spaces
type: Item
instance of: scholarly article
title: Estimates for resolvents and functions of operator pencils on tensor products of Hilbert spaces
zbMATH Open document ID: 1227.47008
DOI: 10.1215/21562261-1299927
published in: Kyoto Journal of Mathematics
publication date: 2011-10-21T00:00:00Z
review text: Let \(X, Y\) be separable Hilbert spaces. The author establishes some norm estimates for the resolvent and operator-valued functions of the operator \(A =\sum_{k=0}^m B_k\otimes S_k\), where \(B_k\,\,(k =0, \dots , m)\) are bounded operators acting on \(Y\) and \(S\) is an invertible selfadjoint operator acting in \(X\). By these estimates, he investigates spectrum perturbations of the operator pencil \(A\). Some improvements are given in the case where \(Y=\mathbb{C}^n\). The author then uses his results to study the non-selfadjoint differential operators with matrix and operator coefficients in Hilbert spaces. The reader may also want to consult \textit{L. A. Shuster} [J. Math. Anal. Appl. 229, No.~2, 363--375 (1999; Zbl 0919.34070)], where the problem of localization of the spectrum for a class of semiregular boundary value problems is investigated.
reviewed by: Mohammad Sal Moslehian
Mathematics Subject Classification ID: 47A80
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 34L15
zbMATH DE Number: 5960767
zbMATH Keywords: Hilbert space
zbMATH Keywords: estimate
zbMATH Keywords: resolvent
zbMATH Keywords: operator pencil
zbMATH Keywords: tensor product
zbMATH Keywords: non-selfadjoint operator
zbMATH Keywords: spectrum perturbation
zbMATH Keywords: differential operator
author: Michael I. Gil'
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/21562261-1299927
OpenAlex ID: W2062573499
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description: scientific article; zbMATH DE number 5960767