An invertibility criterion in a C*-algebra acting on the Hardy space with applications to composition operators
Functional Analysis
2017-09-25 v2 Complex Variables
Operator Algebras
Abstract
In this paper we prove an invertibility criterion for certain operators which is given as a linear algebraic combination of Toeplitz operators and Fourier multipliers acting on the Hardy space of the unit disc. Very similar to the case of Toeplitz operators we prove that such operators are invertible if and only if they are Fredholm and their Fredholm index is zero. As an application we prove that for "quasi-parabolic" composition operators the spectra and the essential spectra are equal.
Keywords
Cite
@article{arxiv.1705.04342,
title = {An invertibility criterion in a C*-algebra acting on the Hardy space with applications to composition operators},
author = {Uğur Gül and Beyaz Başak Koca},
journal= {arXiv preprint arXiv:1705.04342},
year = {2017}
}
Comments
10 pages. arXiv admin note: text overlap with arXiv:1002.4640, arXiv:1205.6054