Perturbation of Browder Spectrum of Upper-triangular Operator Matrices

2013/12/11 by Shifang Zhang, Zhang, Shifang, Huaijie Zhong +3
Computer Science · Mathematics · #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics #math.FA

paper · pdf · doi:10.48550/arxiv.1312.3042

arxiv created 2013/12/11 · arxiv updated 2013/12/12

Abstract

Let M_C=(A · C
0 · B ) is a 2-by-2 upper triangular operator matrix acting on the Banach space X⊕ Y or Hilbert space H⊕ K. For the most import spectra such as spectrum, essential spectrum and Weyl spectrum, the characterizations of the perturbations of M_C on Banach space have been presented. However, the characterization for the Browder spectrum on the Banach space is still unknown. The goal of this paper is to present some necessary and sufficient conditions for M_C to be Browder for some C∈ B(Y,X) by using an alternative approach based on matrix representation of operators and the ghost index theorem. Moreover, in the Hilbert space case the characterizations of the Fredholm and invertible perturbations of Browder spectrum are also given.

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