## Linear Operators: General theory |

### From inside the book

Results 1-3 of 87

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24 ( 242 )

on continuity of limit function , IV . 6 . 11 ( 268 ) remarks concerning , ( 383 )

Ascoli - Arzelą theorem , on compactness of continuous functions , IV . 6 . 7 ( 266

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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 - Arzelą theorem , on compactness of continuous functions , IV . 6 . 7 ( 266

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3 ( 10 )

sphere , II . 3 . 1 ( 59 ) Closure of a set , criterion to be in , 1 . 7 . 2 ( 27 ) definition ,

1 . 4 . 9 ( 11 )

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3 ( 10 )

**properties**, 1 . 4 . 4 – 5 ( 10 ) Closed sphere , II . 4 . 1 ( 70 ) Closed unitsphere , II . 3 . 1 ( 59 ) Closure of a set , criterion to be in , 1 . 7 . 2 ( 27 ) definition ,

1 . 4 . 9 ( 11 )

**properties**of the closure operation , 1 . 4 . 10 – 11 ( 11 - 12 ) Cluster...

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1 . 11 ( 100 - 101 ) Essentially bounded , definition , III . 1 . 11 ( 100 - 101 )

Essentially separably valued , definition , III . 1 . 11 ( 100 - 101 ) Euclidean space

, definition , IV . 2 . 1 ( 238 ) further

real and ...

1 . 11 ( 100 - 101 ) Essentially bounded , definition , III . 1 . 11 ( 100 - 101 )

Essentially separably valued , definition , III . 1 . 11 ( 100 - 101 ) Euclidean space

, definition , IV . 2 . 1 ( 238 ) further

**properties**, IV . 15 study of , IV . 3 Extendedreal and ...

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### Contents

Preliminary Concepts A Settheoretic Preliminaries 1 Notation and Elementary Notions | 1 |

Partially Ordered Systems | 7 |

Exercises | 9 |

Copyright | |

35 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

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