## Linear Operators: Spectral theory |

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Page 893

Thus if E is a bounded

operators in the B-space 3., and if a e 3, then the integral J f(s)|E(ds)w is defined

for every bounded 2-measurable function f on S. It follows immediately that [s ...

Thus if E is a bounded

**additive**set function on 2 whose values E(6) are boundedoperators in the B-space 3., and if a e 3, then the integral J f(s)|E(ds)w is defined

for every bounded 2-measurable function f on S. It follows immediately that [s ...

Page 932

Let S be an abstract set and 2 a field (resp. o-field) of subsets of S. Let F be an

operators on a Hilbert space $5 satisfying F(q) = 0 and F(S) = I. Then there exists

a ...

Let S be an abstract set and 2 a field (resp. o-field) of subsets of S. Let F be an

**additive**(resp. weakly countably**additive**) function on 2 to the set of positiveoperators on a Hilbert space $5 satisfying F(q) = 0 and F(S) = I. Then there exists

a ...

Page 958

To see that u0 is countably

union e is also in 30. Let r ... This argument shows that the vector valued

set function p is weakly countably

To see that u0 is countably

**additive**on 30 let e, n > 1, be disjoint sets in 30 whoseunion e is also in 30. Let r ... This argument shows that the vector valued

**additive**set function p is weakly countably

**additive**on the g-field consisting of all Borel ...### What people are saying - Write a review

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### Contents

SPECTRAL THEORY | 858 |

868 | 885 |

Miscellaneous Applications | 937 |

Copyright | |

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