Regular functions of operators on tensor products of Hilbert spaces

M. I. Gil

doi:10.1007/s00020-004-1359-8

Regular functions of operators on tensor products of Hilbert spaces

M. I. Gil

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

A class of linear operators on tensor products of Hilbert spaces is considered. Estimates for the norm of operator-valued functions regular on the spectrum are derived. These results are new even in the finite-dimensional case. By virtue of the obtained estimates, we derive stability conditions for semilinear differential equations. Applications of the mentioned results to integro-differential equations are also discussed.

Original language	English
Pages (from-to)	317-331
Number of pages	15
Journal	Integral Equations and Operator Theory
Volume	54
Issue number	3
DOIs	https://doi.org/10.1007/s00020-004-1359-8
State	Published - 1 Mar 2006

Keywords

Hilbert spaces
Integro-differential equations
Operator functions
Tensor products

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/s00020-004-1359-8

Cite this

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title = "Regular functions of operators on tensor products of Hilbert spaces",

abstract = "A class of linear operators on tensor products of Hilbert spaces is considered. Estimates for the norm of operator-valued functions regular on the spectrum are derived. These results are new even in the finite-dimensional case. By virtue of the obtained estimates, we derive stability conditions for semilinear differential equations. Applications of the mentioned results to integro-differential equations are also discussed.",

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author = "Gil, \{M. I.\}",

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year = "2006",

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AU - Gil, M. I.

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PY - 2006/3/1

Y1 - 2006/3/1

N2 - A class of linear operators on tensor products of Hilbert spaces is considered. Estimates for the norm of operator-valued functions regular on the spectrum are derived. These results are new even in the finite-dimensional case. By virtue of the obtained estimates, we derive stability conditions for semilinear differential equations. Applications of the mentioned results to integro-differential equations are also discussed.

AB - A class of linear operators on tensor products of Hilbert spaces is considered. Estimates for the norm of operator-valued functions regular on the spectrum are derived. These results are new even in the finite-dimensional case. By virtue of the obtained estimates, we derive stability conditions for semilinear differential equations. Applications of the mentioned results to integro-differential equations are also discussed.

KW - Hilbert spaces

KW - Integro-differential equations

KW - Operator functions

KW - Tensor products

UR - https://www.scopus.com/pages/publications/32944472904

U2 - 10.1007/s00020-004-1359-8

DO - 10.1007/s00020-004-1359-8

M3 - Article

AN - SCOPUS:32944472904

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SP - 317

EP - 331

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 3

ER -

Regular functions of operators on tensor products of Hilbert spaces

Abstract

Keywords

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