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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 373147, 8 pages
http://dx.doi.org/10.1155/2013/373147
Research Article

The Intersection of Upper and Lower Semi-Browder Spectrum of Upper-Triangular Operator Matrices

1School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China
2School of Mathematics, Central South University, Changsha 410075, China

Received 22 January 2013; Accepted 3 August 2013

Academic Editor: Alberto Fiorenza

Copyright © 2013 Shifang Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

When and are given, we denote by the operator acting on the infinite-dimensional separable Hilbert space of the form . In this paper, it is proved that there exists some operator such that is upper semi-Browder if and only if there exists some left invertible operator such that is upper semi-Browder. Moreover, a necessary and sufficient condition for to be upper semi-Browder for some is given, where denotes the subset of all of the invertible operators of .