Browder spectra of upper-triangular operator matrices
type: Item
instance of: scholarly article
title: Browder spectra of upper-triangular operator matrices
zbMATH Open document ID: 1109.47007
author: Haiyan Zhang
author: Hongke Du
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-11-15T00:00:00Z
review text: Let \(M_C=\left[\begin{smallmatrix} A & B\\ O & B\end{smallmatrix}\right]\) be a \(2\times 2\) upper triangular operator matrix acting on the Hilbert space \(H\oplus K\). In this paper, the authors prove, for given operators \(A\) and \(B\), that \[ \bigcup_{C \in L(K,H)}\sigma_b(M_C)=\left(\bigcup_{C\in L(K,H)}\sigma(M_C)\right)\setminus \rho_b(A)\cap\rho_b(B), \] where \(\rho_b(T)=\mathbb{C}\setminus\sigma_b(T)\) denotes the Browder resolvent of an operator \(T\). Moreover, they explore the relations of \(\sigma(A)\cup\sigma(B)\setminus\sigma(M_C)\), \(\sigma_b(A)\cup \sigma_b(B) \setminus\sigma_b(M_C)\) and \(\sigma_w(A)\cup \sigma_w(B)\setminus\sigma_w (M_C)\), where \(\sigma(A)\), \(\sigma_b (A)\) and \(\sigma_w(A)\) denote the spectrum, the Browder spectrum and the Weyl spectrum of \(A\), respectively.
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 5072977
zbMATH Keywords: Browder spectrum
zbMATH Keywords: Weyl spectrum
zbMATH Keywords: upper-triangular operator matrix
reviewed by: Bahmann Yousefi
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.10.073
OpenAlex ID: W2046103227
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DOI: 10.1016/J.JMAA.2005.10.073
description: scientific article; zbMATH DE number 5072977