## Linear Operators: General theory |

### From inside the book

Results 1-3 of 98

Page 838

space of ,

. 17 ( 72 ) Arzelą theorem , on continuity of limit function , IV . 6 . 11 ( 268 )

remarks concerning , ( 383 ) Ascoli - Arcelą theorem , on compactness of

continuous ...

space of ,

**definition**, IV . 2 . 24 ( 242 ) properties , IV . 15 Annihilator of a set , II . 4. 17 ( 72 ) Arzelą theorem , on continuity of limit function , IV . 6 . 11 ( 268 )

remarks concerning , ( 383 ) Ascoli - Arcelą theorem , on compactness of

continuous ...

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H Closed orthonormal system ,

Closed set ,

II . 4 . 1 ( 70 ) Closed unit sphere , II . 3 . 1 ( 59 ) Closure of a set , criterion to be in

, 1 ...

H Closed orthonormal system ,

**definition**, IV . 14 . 1 ( 357 ) study of , IV . 14Closed set ,

**definition**, 1 . 4 . 3 ( 10 ) properties , 1 . 4 . 4 - 5 ( 10 ) Closed sphere ,II . 4 . 1 ( 70 ) Closed unit sphere , II . 3 . 1 ( 59 ) Closure of a set , criterion to be in

, 1 ...

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11 ( 100 - 101 ) Essential singularity ,

17 ( 23 ) ...

11 ( 100 - 101 ) Essential singularity ,

**definition**, ( 229 ) Essential supremum ,**definition**, III . 1 . 11 ( 100 - 101 ) ... 3 Extended real and complex numbers ,**definitions**, ( 3 ) topology of , ( 11 ) Extension of a function , by continuity , 1 . 6 .17 ( 23 ) ...

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### Contents

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Three Basic Principles of Linear Analysis | 49 |

Copyright | |

50 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

analytic applied arbitrary assumed B-space Borel bounded called Chapter clear closed complex condition Consequently constant contains continuous functions continuous linear converges Corollary countably additive defined DEFINITION denote dense determined dimensional disjoint element equation equivalent everywhere Exercise exists extended field finite follows formula function defined function f given Hence Hilbert identity implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear map linear operator linear space meaning metric space neighborhood norm obtained operator positive measure space projection PROOF properties proved range reflexive regular respect satisfies scalar seen separable sequence sequentially set function Show shown statement strongly subset subspace sufficient Suppose Theorem theory tion topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero