## 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

. However , Fixman ( 1 ) proved that the restriction of a spectral operator T to an

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 resolution of 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

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**invariant**...Page 2286

Similarly if K is a closed

A - K n D ( A - 1 ) ) . It follows from Theorem 19 ( b ) and Lemma 35 that M D ( A )

is dense in M. Similarly RD ( A - 1 ) is dense in K. It is conceivable that Ø ( M ) ...

Similarly if K is a closed

**invariant**subspace in H , Y ( ) denotes the closure in X ofA - K n D ( A - 1 ) ) . It follows from Theorem 19 ( b ) and Lemma 35 that M D ( A )

is dense in M. Similarly RD ( A - 1 ) is dense in K. It is conceivable that Ø ( M ) ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

28 other sections not shown

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