Samuel multiplicities and Browder Spectrum of Operator Matrices

Details Samuel multiplicities and Browder Spectrum of Operator Matrices Samuel multiplicities and Browder Spectrum of Operator Matrices

2011-07-02

arxiv.org/abs/1107.0356v1

Mathematics

Functional Analysis

13

Scientific paper

we show that the definitions of some classes of semi-Fredholm operators, which use the language of algebra and first introduced by X. Fang in [8], are equivalent to that of some well-known operator classes. For example, the concept of shift-like semi-Fredholm operator on Hilbert space coincide with that of upper semi-Browder operator. For applications of Samuel multiplicities we characterize the sets of $\bigcap_{C\in B(K,\,H)}\sigma_{ab}(M_{C}),\bigcap_{C\in B(K,\,H)}\sigma_{sb}(M_{C})$ and $\bigcap_{C\in B(K,\,H)}\sigma_{b}(M_{C}),$ respectively, where $M_{C}=({array}{cc}A&C 0&B {array})$ denotes a 2-by-2 upper triangular operator matrix acting on the Hilbert space $H\oplus K$.

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