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$a$-Weyl's theorem for operator matrices

Authors: Young Min Han and Slavisa V. Djordjevic
Journal: Proc. Amer. Math. Soc. 130 (2002), 715-722
MSC (2000): Primary 47A50, 47A53
Published electronically: July 31, 2001
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If $M_{C}=\left(\begin{smallmatrix}A&C\\ 0&B\end{smallmatrix}\right)$ 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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Additional Information

Young Min Han
Affiliation: Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea
Address at time of publication: Department of Mathematics, 14 MacLean Hall, University of Iowa, Iowa City, Iowa 52242-1419

Slavisa V. Djordjevic
Affiliation: Department of Mathematics, Faculty of Philosophy, University of Niš, Ćirila and Metodija 2, 18000 Niš, Yugoslavia

Keywords: Weyl spectrum, essential approximate point spectrum, Browder essential approximate point spectrum, $a$-Weyl's theorem, Weyl's theorem, $a$-Browder's theorem, Browder's theorem
Received by editor(s): February 29, 2000
Received by editor(s) in revised form: August 25, 2000
Published electronically: July 31, 2001
Additional Notes: This work was supported by the Brain Korea 21 Project (through Seoul National University)
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2001 American Mathematical Society