Authors: Ivković, Stefan 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On Upper Triangular Operator 2×2 Matrices Over C∗-Algebras
Journal: Filomat
Volume: 34
Issue: 3
First page: 691
Last page: 706
Issue Date: 2020
Rank: M22
ISSN: 0354-5180
DOI: 10.2298/FIL2003691I
URL: https://www.pmf.ni.ac.rs/filomat-content/2020/34-3/34-3-1-12174.pdf
Abstract: 
We study adjointable, bounded operators on the direct sum of two copies of the standard Hilbert C∗-module over a unital C∗-algebra A that are given by upper triangular 2 by 2 operator matrices. Using thedefinition of A-Fredholm and semi-A-Fredholm operators given in [3], [4], we obtain conditions relating semi-A-Fredholmness of these operators and that of their diagonal entries, thus generalizing the results in [1], [2]. Moreover, we generalize the notion of the spectra of operators by replacing scalars by the elements in the C∗-algebra A.Considering these new spectra in A of bounded, adjointable operators on Hilbert C∗-modules over A related to the classes of A-Fredholm and semi-A-Fredholm operators, we prove ananalogue or a generalized version of the results in [1] concerning the relationship between the spectra of 2 by 2 upper triangular operator matrices and the spectra of their diagonal entries.
Keywords: Hilbert C*- module | semi-A-Fredholm operator | A-Fredholm spectra | perturbations of spectra | essential spectra andoperator matrices
Publisher: Prirodno matematički fakultet, Univerzitet u Nišu

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