Kyoto Journal of Mathematics

Estimates for resolvents and functions of operator pencils on tensor products of Hilbert spaces

M. I. Gil’

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Abstract

Let H=XY be a tensor product of separable Hilbert spaces X and Y. We establish norm estimates for the resolvent and operator-valued functions of the operator A=k=0mBkSk, where Bk (k=0,,m) are bounded operators acting in Y, and S is a self-adjoint operator acting in X. By these estimates we investigate spectrum perturbations of A. The abstract results are applied to the nonself-adjoint differential operators in Hilbert and Euclidean spaces. Our main tool is a combined use of some properties of operators on tensor products of Hilbert spaces and the recent estimates for the norm of the resolvent of a nonself-adjoint operator.

Article information

Source
Kyoto J. Math., Volume 51, Number 3 (2011), 673-686.

Dates
First available in Project Euclid: 1 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1312205243

Digital Object Identifier
doi:10.1215/21562261-1299927

Mathematical Reviews number (MathSciNet)
MR2824004

Zentralblatt MATH identifier
1227.47008

Subjects
Primary: 47A80: Tensor products of operators [See also 46M05] 47E05: Ordinary differential operators [See also 34Bxx, 34Lxx] (should also be assigned at least one other classification number in section 47) 34L15: Eigenvalues, estimation of eigenvalues, upper and lower bounds

Citation

Gil’, M. I. Estimates for resolvents and functions of operator pencils on tensor products of Hilbert spaces. Kyoto J. Math. 51 (2011), no. 3, 673--686. doi:10.1215/21562261-1299927. https://projecteuclid.org/euclid.kjm/1312205243


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