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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Page 1994
Then , by Theorem 4 , ang F - nx , and since an q converges , we see from the continuity of F that > Х m.no O lim lĂr ( s ) — 1 ( ) 2 ds = 0 , which implies ( III.3.6 ) that Ăn converges in measure on o . Conversely , if ( 29 ) and ( 30 ) ...
Then , by Theorem 4 , ang F - nx , and since an q converges , we see from the continuity of F that > Х m.no O lim lĂr ( s ) — 1 ( ) 2 ds = 0 , which implies ( III.3.6 ) that Ăn converges in measure on o . Conversely , if ( 29 ) and ( 30 ) ...
Page 2218
It must be shown that { E , } converges strongly to E. By Lemma 6 , E is in B and so a consideration of the sequence { E. -E } shows that it may be assumed that E 0. Thus , to make an indirect proof , it is assumed that the sequence ...
It must be shown that { E , } converges strongly to E. By Lemma 6 , E is in B and so a consideration of the sequence { E. -E } shows that it may be assumed that E 0. Thus , to make an indirect proof , it is assumed that the sequence ...
Page 2462
Moreover , if C belongs to the trace class C1 , then T , C converges to zero in trace norm , and CT * converges to zero in trace norm . PROOF . The set K = C ( { xe H || 2 < 1 } ) is conditionally compact , and thus for each ε > 0 there ...
Moreover , if C belongs to the trace class C1 , then T , C converges to zero in trace norm , and CT * converges to zero in trace norm . PROOF . The set K = C ( { xe H || 2 < 1 } ) is conditionally compact , and thus for each ε > 0 there ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
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