Linear Operators: General theory |
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Page 289
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 ...
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 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 + ] , .
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 proof of the lemma . Q.E.D. We shall now state and prove the lemma referred to as CPx .
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 .
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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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