## Linear Operators: General theory |

### From inside the book

Results 1-3 of 95

Page 840

Closed orthonormal system ,

set ,

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

Closed orthonormal system ,

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

**definition**, I . 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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17 ( 274 ) remarks on , ( 383 – 385 ) Strictly convex B - space ,

7 ( 458 ) Strong operator topology ,

1 - 5 ( 511 ) , VI . 9 . 1112 ( 512 - 513 ) Strong topology , in a normed space , II .

17 ( 274 ) remarks on , ( 383 – 385 ) Strictly convex B - space ,

**definition**, V . 11 .7 ( 458 ) Strong operator topology ,

**definition**, VI . 1 . 2 ( 475 ) properties , VI . 9 .1 - 5 ( 511 ) , VI . 9 . 1112 ( 512 - 513 ) Strong topology , in a normed space , II .

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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