## Linear Operators: General theory |

### From inside the book

Results 1-3 of 86

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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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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 ...

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 | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

21 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 Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex Consequently constant contains converges convex Corollary defined DEFINITION denote dense determined differential disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math mean measure space metric neighborhood norm positive measure problem Proc projection PROOF properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement strongly subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero