## Linear Operators: General theory |

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Page 91

admits an

admits an

**equivalent**metric under which it is complete , then G admits an invariant metric and is complete under each invariant metric .Page 311

According to Theorems 6.18 and 6.20 there is a compact Hausdorff space S , such that B ( S , E ) is

According to Theorems 6.18 and 6.20 there is a compact Hausdorff space S , such that B ( S , E ) is

**equivalent**to C ( S . ) . Theorem 5.1 shows that there ...Page 347

( b ) Show that L ( S , E , u ) is

( b ) Show that L ( S , E , u ) is

**equivalent**to l , if and only if there exists a countable collection of atoms of finite measure { En } in such that every ...### 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