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
The situation corresponding to an invariant closed subspace of T is not so simple . However , Fixman [ 1 ] proved that the restriction of a spectral operator T to an invariant closed subspace y of X is spectral if and only if the ...
The situation corresponding to an invariant closed subspace of T is not so simple . However , Fixman [ 1 ] proved that the restriction of a spectral operator T to an invariant closed subspace y of X is spectral if and only if the ...
Page 2214
18 THEOREM . Let B be a bounded Boolean algebra of projections in a weakly complete space . Then an operator is in the weakly closed algebra generated by B if and only if it leaves invariant every closed linear manifold which is ...
18 THEOREM . Let B be a bounded Boolean algebra of projections in a weakly complete space . Then an operator is in the weakly closed algebra generated by B if and only if it leaves invariant every closed linear manifold which is ...
Page 2286
Similarly if K is a closed invariant subspace in H , Y ( K ) denotes the closure in X of A - 1Kn D ( A - 1 ) ) . = - 2 It follows from Theorem 19 ( b ) and Lemma 35 that Mn D ( A ) is dense in M. Similarly In D ( A - 1 ) is dense in K.
Similarly if K is a closed invariant subspace in H , Y ( K ) denotes the closure in X of A - 1Kn D ( A - 1 ) ) . = - 2 It follows from Theorem 19 ( b ) and Lemma 35 that Mn D ( A ) is dense in M. Similarly In D ( A - 1 ) is dense in K.
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
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