## 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 ...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 ...Page 511

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

2 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 ...### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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