## Linear Operators, Part 2 |

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Page 897

The spectral measure is

The spectral measure is

**countably additive**in the strong operator topology . Proof . If { On } is a sequence of Borel sets decreasing to the void set then ...Page 932

... of subsets of S. Let F be an additive ( resp . weakly

... of subsets of S. Let F be an additive ( resp . weakly

**countably additive**) ... projection valued additive ( resp . weakly**countable additive**) function E ...Page 958

This argument shows that the vector valued additive set function y is weakly

This argument shows that the vector valued additive set function y is weakly

**countably additive**on the o - field consisting of all Borel subsets of e .### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

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 Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero