Linear Operators: Spectral operators |
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Page 1951
By Corollary V1.5.5 the compact operators form a closed twosided ideal in B ( X ) and so the present corollary is immediate . Q.E.D. 4 COROLLARY . If T is weakly compact , then so are S , N , and every projection E ( o ) with 0 € 0 .
By Corollary V1.5.5 the compact operators form a closed twosided ideal in B ( X ) and so the present corollary is immediate . Q.E.D. 4 COROLLARY . If T is weakly compact , then so are S , N , and every projection E ( o ) with 0 € 0 .
Page 1952
0 0 6 COROLLARY . If A , T = 0 ( respectively TA , = 0 ) , then A , S = A , N = A , E ( 0 ) = 0 if 0 0 0 ( respectively SA , = NA . = E ( 0 ) A , = 0 if 0 € 7 ) . 7 COROLLARY . A spectral operator is of finite type if and only if it is ...
0 0 6 COROLLARY . If A , T = 0 ( respectively TA , = 0 ) , then A , S = A , N = A , E ( 0 ) = 0 if 0 0 0 ( respectively SA , = NA . = E ( 0 ) A , = 0 if 0 € 7 ) . 7 COROLLARY . A spectral operator is of finite type if and only if it is ...
Page 2192
This shows that o ( S ( f ) ) = f ( 0 ) 2 0 $ ( 8 ) E ( O ) = 1 a and completes the proof of the lemma , Q.E.D. 12 COROLLARY . Let A be an algebra of operators in a weakly complete B - space X. Suppose that A is topologically and ...
This shows that o ( S ( f ) ) = f ( 0 ) 2 0 $ ( 8 ) E ( O ) = 1 a and completes the proof of the lemma , Q.E.D. 12 COROLLARY . Let A be an algebra of operators in a weakly complete B - space X. Suppose that A is topologically and ...
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Contents
SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1931 |
Copyright | |
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