## Linear Operators: General theory |

### From inside the book

Results 1-3 of 77

Page 419

Then the l '

form N ( p ; A , € ) { 9 ||| ( p ) -1 ( 9 ) | < E , JE A } , where pe X , A is a finite subset

of T ' , and ε > 0 . The terms I ' - open and I - closed subsets of X , C - continuous ...

Then the l '

**topology**of X is the**topology**obtained by taking as base all sets of theform N ( p ; A , € ) { 9 ||| ( p ) -1 ( 9 ) | < E , JE A } , where pe X , A is a finite subset

of T ' , and ε > 0 . The terms I ' - open and I - closed subsets of X , C - continuous ...

Page 420

Nelson Dunford, Jacob T. Schwartz. in the X *

weakly in the sense of Definition II.3.25 . On the other hand , if X is a subspace of

y * , then each element y e Y determines the linear functional f , on X defined by 1

...

Nelson Dunford, Jacob T. Schwartz. in the X *

**topology**if and only if lim , X. = xweakly in the sense of Definition II.3.25 . On the other hand , if X is a subspace of

y * , then each element y e Y determines the linear functional f , on X defined by 1

...

Page 512

T + is compact in the strong operator

sequentially compact in the weak operator

the weak operator

X , Y ) ...

T + is compact in the strong operator

**topology**. If Y is also separable , A issequentially compact in the weak operator

**topology**if and only if À is compact inthe weak operator

**topology**. 6 If Y is reflexive , then the closed unit sphere of B (X , Y ) ...

### 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 |

quences | 26 |

Copyright | |

81 other sections not shown

### Other editions - View all

### Common terms and phrases

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