## Linear Operators: Spectral theory |

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Page 893

It is clear that if v is a bounded

It is clear that if v is a bounded

**additive**vector valued set function on £ , the integral St ( s ) v ( ds ) of a bounded E - measurable function f may be defined similarly . Thus if E is a bounded**additive**set function on whose values ...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 ( $ ) O and F ( S ) ...Page 958

By a theorem of Pettis ( IV.10.1 ) it is countably

By a theorem of Pettis ( IV.10.1 ) it is countably

**additive**in the strong topology , i.e. , ly ( rm ) / 2 = vorm ) → 0 , and this proves Molin that Mo is countably**additive**on Bo . The set function Mo will now be extended to a ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero