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 1928
Terminology and Preliminary Notions > The concepts of a Boolean algebra of projections , a spectral measure , an integral with respect to a spectral measure , and so on , which have been explained in Section X.1 , are all fundamental ...
Terminology and Preliminary Notions > The concepts of a Boolean algebra of projections , a spectral measure , an integral with respect to a spectral measure , and so on , which have been explained in Section X.1 , are all fundamental ...
Page 2199
If the strongly closed bounded Boolean algebra B of projections is not complete , there is , by the preceding lemma , a vector x and an increasing generalized sequence { Ex } of projections in B such that the limit lima Eqx does not ...
If the strongly closed bounded Boolean algebra B of projections is not complete , there is , by the preceding lemma , a vector x and an increasing generalized sequence { Ex } of projections in B such that the limit lima Eqx does not ...
Page 2218
Every operator in the weakly closed operator algebra generated by a spectral operator of scalar type and the projections in its resolution of the identity is a spectral operator of scalar type . PROOF . Since a spectral operator of ...
Every operator in the weakly closed operator algebra generated by a spectral operator of scalar type and the projections in its resolution of the identity is a spectral operator of scalar type . PROOF . Since a spectral operator of ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
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