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 1983
Then A is a spectral operator of scalar type . PROOF . The argument of the preceding corollary shows that A is a spectral operator . Since  ( s ) has distinct eigenvalues , it is a scalar operator , that is , its radical part is zero ...
Then A is a spectral operator of scalar type . PROOF . The argument of the preceding corollary shows that A is a spectral operator . Since  ( s ) has distinct eigenvalues , it is a scalar operator , that is , its radical part is zero ...
Page 2396
Leto , be as in the preceding lemma , put A ( a ) = Aoli , ula ) ) ) , and let B ( a ) = A ( 04 ( :, u ( a ) ) ) ( cf. Lemma 4 for the definition of u ( a ) ) . Then , by the preceding lemma , by Lemma 1 , and by formulas ( 2a ) and ...
Leto , be as in the preceding lemma , put A ( a ) = Aoli , ula ) ) ) , and let B ( a ) = A ( 04 ( :, u ( a ) ) ) ( cf. Lemma 4 for the definition of u ( a ) ) . Then , by the preceding lemma , by Lemma 1 , and by formulas ( 2a ) and ...
Page 2455
Therefore , if we let the three operators of the preceding lemma be H2 , H1 , H1 , we obtain the present corollary . Q.E.D. 5 COROLLARY . Under the hypotheses of the preceding corollary , U ( H , H , ) is an isometric mapping of < ( H1 ...
Therefore , if we let the three operators of the preceding lemma be H2 , H1 , H1 , we obtain the present corollary . Q.E.D. 5 COROLLARY . Under the hypotheses of the preceding corollary , U ( H , H , ) is an isometric mapping of < ( H1 ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
47 other sections not shown
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