Spectra of Upper-triangular Operator Matrix

Details Spectra of Upper-triangular Operator Matrix Spectra of Upper-triangular Operator Matrix

2009-06-27

arxiv.org/abs/0906.5055v1

Mathematics

Functional Analysis

Scientific paper

Let $X$ and $Y$ be Banach spaces, $A\in B(X)$, $B\in B(Y)$, $C\in B(Y, X)$, $M_{C}=({cc}A&C 0&B)$ be the operator matrix acting on the Banach space $X\oplus Y$. In this paper, we give out 20 kind spectra structure of $M_C$, decide 18 kind spectra filling-in-hole properties of $M_C$, and present 10 examples to show that some conclusions about the spectra structure or filling-in-hole properties of $M_C$ are not true.

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