## Linear Operators: Spectral theory |

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Page 888

where o , d are arbitrary spectral sets and where ® is the void set . ... This

observation leads to the notion of a

...

where o , d are arbitrary spectral sets and where ® is the void set . ... This

observation leads to the notion of a

**spectral measure**in a B - space X . A**spectral****measure**in X is a homomorphic map of a Boolean algebra of sets into a Boolean...

Page 889

5 ) , every set in the domain of a

an open and closed subset of o ( T ) and thus a spectral set . However , in order

to reduce the study of T to its study on invariant subspaces in which it has a

smaller ...

5 ) , every set in the domain of a

**spectral measure**satisfying ( iii ) is necessarilyan open and closed subset of o ( T ) and thus a spectral set . However , in order

to reduce the study of T to its study on invariant subspaces in which it has a

smaller ...

Page 897

It follows then from ( iii ) that the projections E ( d ) also commute with T ( f ) and

this completes the proof of the theorem . Q . E . D . 3 COROLLARY . The

...

It follows then from ( iii ) that the projections E ( d ) also commute with T ( f ) and

this completes the proof of the theorem . Q . E . D . 3 COROLLARY . The

**spectral****measure**is countably additive in the strong operator topology . Proof . If { 8n } is a...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

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