𝑎-Weyl’s theorem for operator matrices

Han, Young Min; Djordjević, Slaviša

doi:10.1090/S0002-9939-01-06110-X

$a$-Weyl’s theorem for operator matrices
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by Young Min Han and Slaviša V. Djordjević PDF

Proc. Amer. Math. Soc. 130 (2002), 715-722 Request permission

Abstract:

If $M_{C}=\left (\begin {smallmatrix}A&C0&B\end {smallmatrix}\right )$ is a $2\times 2$ upper triangular matrix on the Hilbert space $H\oplus K$, then $a$-Weyl’s theorem for $A$ and $B$ need not imply $a$-Weyl’s theorem for $M_{C}$, even when $C=0$. In this note we explore how $a$-Weyl’s theorem and $a$-Browder’s theorem survive for $2\times 2$ operator matrices on the Hilbert space.

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