On compressions and generalized spectra of operators over C*-algebras
Functional Analysis
2020-01-09 v1
Abstract
In the classical operator theory, there are several versions of spectra, related to special classes of operators (Fredholm, semi-Fredholm, upper/lower semi-Fredholm,etc.). We generalize these notions for adjointable operators on Hilbert C*-modules replacing scalars by the center of the algebra, and show that most relations between these spectra are still true for these generalized versions. The relation between these spectra of an operator and those of its compressions is also transferred to the case of Hilbert C*-modules.
Keywords
Cite
@article{arxiv.1910.10145,
title = {On compressions and generalized spectra of operators over C*-algebras},
author = {Stefan Ivkovic},
journal= {arXiv preprint arXiv:1910.10145},
year = {2020}
}
Comments
This paper has been accepted by Annals of Functional Analysis in 2019. arXiv admin note: substantial text overlap with arXiv:1906.05359, arXiv:1906.03319