## Linear Operators: Spectral theory |

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Page 893

It is clear that if v is a bounded

integral St ( s ) u ( ds ) of a bounded E - measurable function f may be defined

similarly . Thus if E is a bounded

...

It is clear that if v is a bounded

**additive**vector valued set function on £ , theintegral St ( s ) u ( ds ) of a bounded E - measurable function f may be defined

similarly . Thus if E is a bounded

**additive**set function on £ whose values Ed ) are...

Page 932

Let S be an abstract set and 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 ) = I . Then there

exists ...

Let S be an abstract set and 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 ) = I . Then there

exists ...

Page 958

Hence if e , and eg are disjoint then yley u ez ) = E ( e u ez ) y ( e , u ez ) = [ E ( 41

) + E ( ez ) ] y ( e , u ez ) = E ( e ) y ( e , u ex ) + E ( e ) y ( e , u ez ) = ylez ) + ylez ) ,

so that the vector valued set function y is

Hence if e , and eg are disjoint then yley u ez ) = E ( e u ez ) y ( e , u ez ) = [ E ( 41

) + E ( ez ) ] y ( e , u ez ) = E ( e ) y ( e , u ex ) + E ( e ) y ( e , u ez ) = ylez ) + ylez ) ,

so that the vector valued set function y is

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

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

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