Abstract and Applied Analysis

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

Shifang Zhang, Huaijie Zhong, and Long Long

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Abstract

When A B ( H ) and B B ( K ) are given, we denote by M C the operator acting on the infinite-dimensional separable Hilbert space H K of the form M C = ( A C 0 B ) . In this paper, it is proved that there exists some operator C B ( K , H ) such that M C is upper semi-Browder if and only if there exists some left invertible operator C B ( K , H ) such that M C is upper semi-Browder. Moreover, a necessary and sufficient condition for M C to be upper semi-Browder for some C G ( K , H ) is given, where G ( K , H ) denotes the subset of all of the invertible operators of B ( K , H ) .

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 373147, 8 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393512029

Digital Object Identifier
doi:10.1155/2013/373147

Mathematical Reviews number (MathSciNet)
MR3096835

Zentralblatt MATH identifier
1318.47007

Citation

Zhang, Shifang; Zhong, Huaijie; Long, Long. The Intersection of Upper and Lower Semi-Browder Spectrum of Upper-Triangular Operator Matrices. Abstr. Appl. Anal. 2013 (2013), Article ID 373147, 8 pages. doi:10.1155/2013/373147. https://projecteuclid.org/euclid.aaa/1393512029


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