## Linear Operators: Spectral theory |

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Page 893

Returning now to the general integral | ( 8 ) E ( ds ) where E is merely a bounded

defined in terms of the uniform operator topology . It is clear that if v is a bounded

...

Returning now to the general integral | ( 8 ) E ( ds ) where E is merely a bounded

**additive**operator valued set function , we observe that the integral has beendefined in terms of the uniform operator topology . It is clear that if v is a bounded

...

Page 932

Let S be an abstract set and E a field ( resp . o - field ) of subsets of S. Let F be an

operators on a Hilbert space H satisfying F ( $ ) = 0 and F ( S ) = 1 . Then there

exists ...

Let S be an abstract set and E a field ( resp . o - field ) of subsets of S. Let F be an

**additive**( resp . weakly countably**additive**) function on to the set of positiveoperators on a Hilbert space H satisfying F ( $ ) = 0 and F ( S ) = 1 . Then there

exists ...

Page 958

Hence if e , and eg are disjoint then yleq u ez ) = Ele ; u ez ) yle , u ez ) [ E ( e ) +

E ( ez ) ] yle , u ez ) E ( en ) y ( e , u ez ) + E ( ez ) y ( e , vez ) = v ( e ) + v ( eg ) , so

that the vector valued set function y is

Hence if e , and eg are disjoint then yleq u ez ) = Ele ; u ez ) yle , u ez ) [ E ( e ) +

E ( ez ) ] yle , u ez ) E ( en ) y ( e , u ez ) + E ( ez ) y ( e , vez ) = v ( e ) + v ( eg ) , so

that the vector valued set function y is

**additive**on B. Therefore , if eney = $ , the ...### What people are saying - Write a review

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Copyright | |

57 other sections not shown

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