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

Shifang Zhang, Huaijie Zhong and Long Long

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: When A ∈ B(H) and B ∈ B(K) are given, we denote by MC the operator acting on the infinite‐dimensional separable Hilbert space H ⊕ K of the form MC=(AC0B). In this paper, it is proved that there exists some operator C ∈ B(K, H) such that MC is upper semi‐Browder if and only if there exists some left invertible operator C ∈ B(K, H) such that MC is upper semi‐Browder. Moreover, a necessary and sufficient condition for MC 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).

Date: 2013
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https://doi.org/10.1155/2013/373147

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:373147

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