## Linear Operators: General theory |

### From inside the book

Results 1-3 of 72

Page 477

strong , and the

uniform operator topology is stronger than the strong operator topology , and that

the strong operator topology is stronger than the

...

strong , and the

**weak**operator topologies in B ( x , y ) . It is evident that theuniform operator topology is stronger than the strong operator topology , and that

the strong operator topology is stronger than the

**weak**operator topology . With its...

Page 511

2 A set AC B ( X , Y ) is compact in the

closed in the

compact for each x € X . A set AC B ( X , Y ) is compact in the strong operator

topology if ...

2 A set AC B ( X , Y ) is compact in the

**weak**operator topology if and only if it isclosed in the

**weak**operator topology and the**weak**closure of Ax is weaklycompact for each x € X . A set AC B ( X , Y ) is compact in the strong operator

topology if ...

Page 512

If Y is also separable , A is sequentially compact in the

and only if A is compact in the

the closed unit sphere of B ( X , Y ) is compact in the

If Y is also separable , A is sequentially compact in the

**weak**operator topology ifand only if A is compact in the

**weak**operator topology . 6 If Y is reflexive , thenthe closed unit sphere of B ( X , Y ) is compact in the

**weak**operator topology .### What people are saying - Write a review

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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