Abstract
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.
Citation
M. I. Gil’. "Estimates for resolvents and functions of operator pencils on tensor products of Hilbert spaces." Kyoto J. Math. 51 (3) 673 - 686, Fall 2011. https://doi.org/10.1215/21562261-1299927
Information