Fredholm consistency of upper-triangular operator matrices
type: Item
instance of: scholarly article
title: Fredholm consistency of upper-triangular operator matrices
DOI: 10.4171/JST/184
author: Dragana Cvetković-Ilić
published in: Journal of Spectral Theory
publication date: 2018-01-26T00:00:00Z
review text: Summary: In this paper, for given operators \(A\in\mathcal{B}(\mathcal{H})\) and \(B\in\mathcal{B}(\mathcal{K})\), we characterize the set of all \(C\in\mathcal{B}(\mathcal{K},\mathcal{H})\) such that the operator matrix \(M_C=\begin{bmatrix} A&C\\0&B\end{bmatrix}\) is Fredholm consistent. We completely describe the sets \(\bigcap_{C\in\mathcal{B}(\mathcal{K},\mathcal{H})}\sigma_{\mathrm{FC}}(M_C)\) and \(\bigcup_{C\in\mathcal{B}(\mathcal{K},\mathcal{H})}\sigma_{\mathrm{FC}}(M_C)\). Also, we prove that \(\bigcap_{C\in\mathcal{B}(\mathcal{K},\mathcal{H})}\sigma_{\mathrm{FC}}(M_C)=\sigma_{\mathrm{FC}}(M_0)\).
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 47A53
zbMATH DE Number: 6830234
zbMATH Keywords: Fredholm operator
zbMATH Keywords: Fredholm consistent operator
zbMATH Keywords: upper-triangular operator
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/jst/184
OpenAlex ID: W2775069667
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description: scientific article; zbMATH DE number 6830234