## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 85

Page 419

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. 2

DEFINITION . Let X be a linear vector space , and let I be a total subspace of X * .

Then the l '

form ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. 2

DEFINITION . Let X be a linear vector space , and let I be a total subspace of X * .

Then the l '

**topology**of X is the**topology**obtained by taking as base all sets of theform ...

Page 420

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. in the X *

other hand , if X is a subspace of y * , then each element y e Y determines the ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. in the X *

**topology**if and only if lim , xe = x weakly in the sense of Definition II.3.25 . On theother hand , if X is a subspace of y * , then each element y e Y determines the ...

Page 477

strong , and the weak operator

uniform operator

the strong operator

...

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 thatthe strong operator

**topology**is stronger than the weak operator**topology**. With its...

### What people are saying - Write a review

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

### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

### Other editions - View all

### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero