## Linear Operators: Spectral theory |

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Page 1803

On some

generalization of a theorem of Lebesgue . ... On the basis of a family of

completely additive functions of sets and on the

and equi ...

On some

**properties**of completely additive set functions and their application togeneralization of a theorem of Lebesgue . ... On the basis of a family of

completely additive functions of sets and on the

**properties**of uniform additivityand equi ...

Page 1900

Almost periodic functions , definition , IV . 2 . 25 ( 242 ) space of , additional

– 387 ) study of , IV . 7 Almost uniform ( or u - uniform convergence ) definition , III

. 6 .

Almost periodic functions , definition , IV . 2 . 25 ( 242 ) space of , additional

**properties**, IV . 15 ( 879 ) definition , IV . 2 . 25 ( 242 ) remarks concerning , ( 386– 387 ) study of , IV . 7 Almost uniform ( or u - uniform convergence ) definition , III

. 6 .

Page 1902

Category theorem , of Baire , 1 . 6 . 9 ( 20 ) Cauchy integral formula , ( 227 ) for

functions of an operator , in a finite dimensional space , VII . 1 . 10 ( 560 ) in ...

**properties**, I . 3 . 12 – 14 ( 9 ) Cartesian product of topological spaces , 1 . 8 ( 31 )Category theorem , of Baire , 1 . 6 . 9 ( 20 ) Cauchy integral formula , ( 227 ) for

functions of an operator , in a finite dimensional space , VII . 1 . 10 ( 560 ) in ...

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### 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 consider constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function 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