## Linear Operators: General theory |

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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 æ * \ 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 - u - 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 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

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