## Linear Operators: Spectral theory |

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Page 893

Returning now to the general integral / ( s ) 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 / ( s ) 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

Sz . - Nagy ' s original proof depended on the following theorem due to Neumark

( 3 ] . THEOREM . Let S be an abstract set and E a field ( resp . o - field ) of

subsets of S . Let F be an

E to ...

Sz . - Nagy ' s original proof depended on the following theorem due to Neumark

( 3 ] . THEOREM . 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 onE to ...

Page 958

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

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

that the vector valued set function y is

...

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

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

that the vector valued set function y is

**additive**on By . Therefore , if en ég = $ , the...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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