## Linear Operators: General theory |

### From inside the book

Results 1-3 of 81

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 .Page 858

9 ( 7 ) Wiener measure space , ( 405 ,

67 ) properties , II . 3 . 26 – 27 ( 68 ) in special spaces , IV . 15

additivity , definition , ( 318 ) and strong , IV . 10 . 1 ( 318 )

II .

9 ( 7 ) Wiener measure space , ( 405 ,

**Weak**convergence , definition , II . 3 . 25 (67 ) properties , II . 3 . 26 – 27 ( 68 ) in special spaces , IV . 15

**Weak**countableadditivity , definition , ( 318 ) and strong , IV . 10 . 1 ( 318 )

**Weak**limit , definition ,II .

### What people are saying - Write a review

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

### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

31 other sections not shown

### Other editions - View all

### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional 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 neighborhood norm operator operator topology problem projection PROOF properties proved range reflexive representation respect satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero