## Linear Operators, Part 1 |

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Page 289

felp 3

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 = { $ + ( 8 ) g ( s ) u ( ds ) ...

felp 3

**Proof**. Let æ ** € ( L * ) * . By Theorem 1 , L * is isometrically isomorphic toLą , 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 = { $ + ( 8 ) g ( s ) u ( ds ) ...

Page 434

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

construct a subsequence { ym } of { xn } such that lim , exists for each x * in the set

H of that

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

**proof**of the preceding theorem toconstruct a subsequence { ym } of { xn } such that lim , exists for each x * in the set

H of that

**proof**. Let Km co { ym , Ym + ] , ... } and let yo be an arbitrary point in n ...Page 699

2 v 1 Jo 26 - V + p V t - * - » ) So Va 2y2 2 e dy 2e - v't which proves ( * ) and

completes the

lemma referred to as CPx . For technical reasons occurring later the following

lemma is ...

2 v 1 Jo 26 - V + p V t - * - » ) So Va 2y2 2 e dy 2e - v't which proves ( * ) and

completes the

**proof**of the lemma . Q.E.D. We shall now state and prove thelemma referred to as CPx . For technical reasons occurring later the following

lemma is ...

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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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