## Linear Operators: Spectral theory |

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Page 893

Returning now to the general integral 5 / ( s ) E ( ds ) where E is merely a bounded

Returning now to the general integral 5 / ( s ) E ( ds ) where E is merely a bounded

**additive**operator valued set function , we observe that the integral has been defined in terms of the uniform operator topology .Page 932

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

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 E to the set of positive operators on a Hilbert space y satisfying F ( 0 ) = 0 and F ( S ) ...Page 958

This argument shows that the vector valued

This argument shows that the vector valued

**additive**set function y is weakly countably**additive**on the o - field ... By a theorem of Pettis ( IV.10.1 ) it is countably**additive**in the strong topology , i.e. , ( ( r ) = uo ( rn ) → 0 ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Miscellaneous Applications | 937 |

Compact Groups | 945 |

Copyright | |

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