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Weyl spectra of operator matrices
Authors:Woo Young Lee
Affiliation:Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea
Abstract:

In this paper it is shown that if $M_{C}=left (begin{smallmatrix}A&C 0&Bend{smallmatrix}right )$ is a $2times 2$ upper triangular operator matrix acting on the Hilbert space $mathcal{H}oplus mathcal{K}$ and if $omega (cdot )$ denotes the ``Weyl spectrum", then the passage from $omega (A)cup omega (B)$ to $omega (M_{C})$ is accomplished by removing certain open subsets of $omega (A) cap omega (B)$ from the former, that is, there is equality begin{equation*}omega (A)cup omega (B)=omega (M_{C}) cup mathfrak{S}, end{equation*} where $mathfrak{S}$ is the union of certain of the holes in $omega (M_{C})$ which happen to be subsets of $omega (A)cap omega (B)$.

Keywords:Weyl spectrum   Weyl's theorem   operator matrices
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