## Linear Operators, Part 1 |

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Page 430

There is at least one other type of

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

**weak**compactness that is occasionally of use .Page 477

strong , and the

uniform operator topology is stronger than the strong operator topology , and that

the strong operator topology is stronger than the

...

strong , and the

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

the strong operator topology is stronger than the

**weak**operator topology . With its...

Page 511

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

closed in the

compact for each x € X. A set AC B ( X , Y ) is compact in the strong operator

topology if ...

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

**weak**operator topology if and only if it isclosed in the

**weak**operator topology and the**weak**closure of Ax is weaklycompact for each x € X. A set AC B ( X , Y ) is compact in the strong operator

topology if ...

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 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 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