## 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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Results 1-3 of 89

Page 1928

Terminology and Preliminary Notions The concepts of a Boolean algebra of

and so on , which have been explained in Section X . 1 , are all fundamental for

the ...

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 for

the ...

Page 2218

Every operator in the weakly closed operator algebra generated by a spectral

operator of scalar type and the

spectral operator of scalar type . Proof . Since a spectral operator of scalar type is

...

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 aspectral operator of scalar type . Proof . Since a spectral operator of scalar type is

...

Page 2300

Then , since the collection of finite sums of

bounded , it is clear from [ * ] that the collection of finite sums of

; T + P ) , n 2 K , is uniformly bounded . Moreover , Erap ( Elan ; T ) – Elun ; T + P ...

Then , since the collection of finite sums of

**projections**E ( n ; T ' ) is uniformlybounded , it is clear from [ * ] that the collection of finite sums of

**projections**E ( Mn; T + P ) , n 2 K , is uniformly bounded . Moreover , Erap ( Elan ; T ) – Elun ; T + P ...

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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