Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 51, Number 3 (2011), 673-686.
Estimates for resolvents and functions of operator pencils on tensor products of Hilbert spaces
Let be a tensor product of separable Hilbert spaces and . We establish norm estimates for the resolvent and operator-valued functions of the operator , where are bounded operators acting in , and is a self-adjoint operator acting in . By these estimates we investigate spectrum perturbations of . 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.
Kyoto J. Math., Volume 51, Number 3 (2011), 673-686.
First available in Project Euclid: 1 August 2011
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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