## 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 . Thus every complete linear metric space can be metrized to be an F - space .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 is an isometric isomorphism x * 4 u between B * ( S , E ) and ba ( S , E ) , which ...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 measurable subset of S - un En is either an atom of infinite measure or a null ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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### Common terms and phrases

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