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 .
"The Intersection of Upper and Lower Semi-Browder Spectrum of Upper-Triangular Operator Matrices." Abstr. Appl. Anal. 2013 1 - 8, 2013. https://doi.org/10.1155/2013/373147