## Linear Operators: General theory |

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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 e 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

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

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### 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