## Linear Operators: General theory |

### From inside the book

Results 1-3 of 84

Page 484

Linear combinations of

Linear combinations of

**weakly compact**operators are**weakly compact**. The product of a**weakly compact**linear operator and a bounded linear operator is**weakly compact**. PROOF . Let T , U € B ( X , Y ) , We B ( Y , 3 ) , V € B ( 3 , X ) ...Page 507

Let ( S , E , u ) be a o - finite positive measure space , and let T be a

Let ( S , E , u ) be a o - finite positive measure space , and let T be a

**weakly compact**operator on L ( S , E , u ) to a separable subset of the B - space X. Then there exists a u - essentially unique bounded measurable function x ...Page 540

operator and the operator mapping into a weakly complete space X.

operator and the operator mapping into a weakly complete space X.

**Weakly compact**operators from C [ 0 , 1 ] to X were treated by Sirvint [ 3 ] . A very incisive discussion of**weakly compact**operators with domain C ( S ) was given by ...### 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 | |

91 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 closure complex condition Consequently contains continuous functions converges Corollary defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function f given Hence Hilbert space implies integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space linear topological space Math means measure space metric space neighborhood norm open set operator problem Proc projection Proof properties proved range reflexive respect Russian 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