## Linear Operators: General theory |

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Page 12

The set Ā is the

The set Ā is the

**closure**of A in this topology . PROOF . Statements 10 ( b ) , ( d ) show that 6 , X € F , and 10 ( a ) shows that AUBE F if A , B € F. It follows that any finite union of sets in F is in F. From 10 ( a ) , it follows ...Page 432

To see this , let m be an arbitrary integer ; since x ** is in the X * -

To see this , let m be an arbitrary integer ; since x ** is in the X * -

**closure**of x ( A ) , there is an element zm € A such that 2 * ( cm ) - ** ( * ) < 1m , i 1 , ... , n . Since A is weakly sequentially compact , a subsequence of ...Page 511

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

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 | |

87 other sections not shown

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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