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 2094
It follows from some results of Bade [ 4 ] ( see also XVII.2.1 and XVII.2.12 ) that if X is a weakly complete B - space , then any prespectral operator is automatically spectral , and so has a unique resolution of the identity .
It follows from some results of Bade [ 4 ] ( see also XVII.2.1 and XVII.2.12 ) that if X is a weakly complete B - space , then any prespectral operator is automatically spectral , and so has a unique resolution of the identity .
Page 2143
Let T be a bounded linear operator in the complex B - space X. Then there is a unique spectral measure on the field S ( T ) with the properties = E ( 8 ) x = x , = 0 , SES ( T ) , ( x ) So , de S ( T ) , g ( x ) = 8 ' .
Let T be a bounded linear operator in the complex B - space X. Then there is a unique spectral measure on the field S ( T ) with the properties = E ( 8 ) x = x , = 0 , SES ( T ) , ( x ) So , de S ( T ) , g ( x ) = 8 ' .
Page 2184
It will be seen in the following theorem that an arbitrary isomorphic homeomorphism of the algebra A ( B ) onto the algebra of continuous functions on its structure space may be represented by an integral with respect to a uniquely ...
It will be seen in the following theorem that an arbitrary isomorphic homeomorphism of the algebra A ( B ) onto the algebra of continuous functions on its structure space may be represented by an integral with respect to a uniquely ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
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