Open AccessResolvents of functions of operators with Hilbert-Schmidt hermitian components
Author(s) -
Michael Gil
Publication year - 2018
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1814937g
Subject(s) - mathematics , quasinormal operator , hermitian adjoint , finite rank operator , hermitian matrix , multiplication operator , operator (biology) , hilbert space , operator norm , compact operator , holomorphic function , bounded operator , shift operator , pure mathematics , operator theory , spectrum (functional analysis) , nuclear operator , separable space , mathematical analysis , convex hull , regular polygon , banach space , repressor , chemistry , computer science , biochemistry , geometry , quantum mechanics , transcription factor , programming language , physics , extension (predicate logic) , gene
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.