WEYL SPECTRUM OF THE PRODUCTS OF OPERATORS

Title & Authors
WEYL SPECTRUM OF THE PRODUCTS OF OPERATORS
Cao, Xiaohong;

Abstract
Let $\small{M_C=$$\array{A}$$\small{&}$$\small{C\\0}$$\small{&}$$\small{B}$$}$ be a $\small{2{\times}2}$ upper triangular operator matrix acting on the Hilbert space $\small{H{\bigoplus}K\;and\;let\;{\sigma}_w(\cdot)}$ denote the Weyl spectrum. We give the necessary and sufficient conditions for operators A and B which $\small{{\sigma}_w$$\array{A}$$\small{&}$$\small{C\\0}$$\small{&}$$\small{B}$$={\sigma}_w$$\array{A}$$\small{&}$$\small{C\\0}$$\small{&}$$\small{B}$$\;or\;{\sigma}_w$$\array{A}$$\small{&}$$\small{C\\0}$$\small{&}$$\small{B}$$={\sigma}_w(A){\cup}{\sigma}_w(B)}$ holds for every $\small{C{\in}B(K,\;H)}$. We also study the Weyl's theorem for operator matrices.
Keywords
Weyl spectrum;Weyl's theorem;Browder's theorem;essential approximate point spectrum;
Language
English
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