## Linear Operators: General theory |

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felp 3

felp 3

**Proof**. Let x ** € ( L * ) * . By Theorem 1 , L * is isometrically isomorphic to Lą , so that there is a functional y * € L * such that *** ( ** ) = y * ( g ) when g and r * are connected , as in Theorem 1 , by the formula ** 1 ...Page 434

x * ym and proceed as in the first part of the

x * ym and proceed as in the first part of the

**proof**of the preceding theorem to construct a subsequence { ym } of { xn } such that lim , exists for each x * in the set H of that**proof**. Let Km co { ym , Ym + ] , .Page 699

2 v 1 Jo 26 - V + p V t - * - » ) So Va 2y2 e - Vt ammad dx 21 Jo X - 3 / 2 2 e dy 2e - v't --- A - évt , V1 which proves ( * ) and completes the

2 v 1 Jo 26 - V + p V t - * - » ) So Va 2y2 e - Vt ammad dx 21 Jo X - 3 / 2 2 e dy 2e - v't --- A - évt , V1 which proves ( * ) and completes the

**proof**of the lemma . Q.E.D. We shall now state and prove the lemma referred to as CPx .### 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