## Linear Operators: General theory |

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Page 430

**Weak**Topologies .**Weak**Compactness We have already introduced and employed the concepts of**weak**sequential compactness ( II.3.25 ) and compactness in the X * ( or**weak**) topology . There is at least one other type of**weak**compactness ...Page 477

strong , and the

strong , and the

**weak**operator topologies in B ( X , Y ) . It is evident that the uniform operator topology is stronger than the strong operator topology , and that the strong operator topology is stronger than the**weak**operator ...Page 511

A set AC B ( X , Y ) is compact in the

A set AC B ( X , Y ) is compact in the

**weak**operator topology if and only if it is closed in the**weak**operator topology and the**weak**closure of Ax is weakly compact for each x € X. A set AC B ( X , Y ) is compact in the strong operator ...### 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 | |

91 other sections not shown

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### 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