## Linear Operators: General theory |

### From inside the book

Results 1-3 of 92

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 .

Page 844

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 ) ...

Page 856

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

7 ( 458 ) Strong operator topology ,

1 - 5 ( 511 ) , V1 . 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 ) , V1 . 9 . 1112 ( 512 - 513 ) Strong topology , in a normed space , II .

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### 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