## Linear Operators: General theory |

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Page 494

From IV.10.2 we conclude that T * maps the unit sphere of X * into a conditionally

From IV.10.2 we conclude that T * maps the unit sphere of X * into a conditionally

**weakly compact**set of rca ( S ) ... I T is a**weakly compact**operator from C ( S ) to X , then T sends weak Cauchy sequences into strongly convergent ...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 æ ...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 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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