## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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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 to the set of positive operators on a Hilbert space H satisfying F ( $ ) = 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. , lv ( rm ) / 2 = wolrn ...Page 1803

On some properties of completely

On some properties of completely

**additive**set functions and their application to generalization of a theorem of Lebesgue . Mat . Sbornik N. S. 20 ( 62 ) , 317–329 ( 1947 ) . ( Russian , English summary ) Math . Rev. 9 , 19 ( 1948 ) .### 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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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### Common terms and phrases

additive adjoint operator 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