Linear Operators: Spectral operators |
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Page 1951
Q . E . D 3 COROLLARY . If T is compact , then so are S , N , and every projection
E ( 0 ) with 0 € 7 . PROOF . By Corollary VI . 5 . 5 the compact operators form a
closed twosided ideal in B ( X ) and so the present corollary is immediate .
Q . E . D 3 COROLLARY . If T is compact , then so are S , N , and every projection
E ( 0 ) with 0 € 7 . PROOF . By Corollary VI . 5 . 5 the compact operators form a
closed twosided ideal in B ( X ) and so the present corollary is immediate .
Page 1952
6 COROLLARY . If A , T = 0 ( respectively TA . = 0 ) , then A . S = AN = A , E ( 0 ) =
0 if 0 € 7 ( respectively SA , = NA , = E ( 0 ) A , = 0 if 087 ) . 7 COROLLARY . A
spectral operator is of finite type if and only if it is annihilated by some power of its
...
6 COROLLARY . If A , T = 0 ( respectively TA . = 0 ) , then A . S = AN = A , E ( 0 ) =
0 if 0 € 7 ( respectively SA , = NA , = E ( 0 ) A , = 0 if 087 ) . 7 COROLLARY . A
spectral operator is of finite type if and only if it is annihilated by some power of its
...
Page 2192
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 algebraically
isomorphic to some B - algebra of bounded continuous functions . Then every
operator in A is a ...
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 algebraically
isomorphic to some B - algebra of bounded continuous functions . Then every
operator in A is a ...
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Contents
SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
29 other sections not shown
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