Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Results 1-3 of 88
Page 1953
PROOF . If either AT = 0 or TA = 0 then , by the theorem , either A = AE ( { 0 } ) or A = E ( { 0 } ) A . Thus A = 0 . Q.E.D. 12 COROLLARY . If E ( { a } ) = 0 , then ( 21 – T ' ) X is dense in X. Proof . First suppose that = 0 .
PROOF . If either AT = 0 or TA = 0 then , by the theorem , either A = AE ( { 0 } ) or A = E ( { 0 } ) A . Thus A = 0 . Q.E.D. 12 COROLLARY . If E ( { a } ) = 0 , then ( 21 – T ' ) X is dense in X. Proof . First suppose that = 0 .
Page 2137
Even though ( A ) is taken as a standing assumption throughout this section , it will be indicated parenthetically in the statement of each lemma in the proof of which it is used . 1 LEMMA ( A ) . If a , ß are complex numbers and x ...
Even though ( A ) is taken as a standing assumption throughout this section , it will be indicated parenthetically in the statement of each lemma in the proof of which it is used . 1 LEMMA ( A ) . If a , ß are complex numbers and x ...
Page 2192
This shows that o ( S ( f ) ) 2f ( o ) 2 n f ( 8 ) E ( ) = 1 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 ) ) 2f ( o ) 2 n f ( 8 ) E ( ) = 1 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 | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
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