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http://dx.doi.org/10.4134/JKMS.2008.45.3.771

WEYL SPECTRUM OF THE PRODUCTS OF OPERATORS  

Cao, Xiaohong (College of Mathematics and Information Science Shaanxi Normal University)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.3, 2008 , pp. 771-780 More about this Journal
Abstract
Let $M_C=\(\array{A&C\\0&B}\)$ be a $2{\times}2$ upper triangular operator matrix acting on the Hilbert space $H{\bigoplus}K\;and\;let\;{\sigma}_w(\cdot)$ denote the Weyl spectrum. We give the necessary and sufficient conditions for operators A and B which ${\sigma}_w\(\array{A&C\\0&B}\)={\sigma}_w\(\array{A&C\\0&B}\)\;or\;{\sigma}_w\(\array{A&C\\0&B}\)={\sigma}_w(A){\cup}{\sigma}_w(B)$ holds for every $C{\in}B(K,\;H)$. We also study the Weyl's theorem for operator matrices.
Keywords
Weyl spectrum; Weyl's theorem; Browder's theorem; essential approximate point spectrum;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
Times Cited By Web Of Science : 1  (Related Records In Web of Science)
Times Cited By SCOPUS : 1
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