Resolvents of functions of operators with Hilbert-Schmidt hermitian components
Abstract
Let H be a separable Hilbert space with the unit operator I. We derive a
sharp norm estimate for the operator function (?I-f(A))-1 (? ? C),
where A is a bounded linear operator in H whose Hermitian component (A-
A*)/2i is a Hilbert-Schmidt operator and f(z) is a function holomorphic on
the convex hull of the spectrum of A. Here A* is the operator adjoint to A.
Applications of the obtained estimate to perturbations of operator
equations, whose coefficients are operator functions and localization of
spectra are also discussed.
Publisher
National Library of Serbia
Subject
General Mathematics