## Linear Operators: General theory |

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Page 26

Each notion of convergence

Each notion of convergence

**gives**rise to a related notion of uniform convergence , For instance , let D be a directed set , A an arbitrary set , and X a ...Page 247

Since En = 1 " , the following theorem

Since En = 1 " , the following theorem

**gives**the desired results : 9 THEOREM . If1 < p Soo and p - 1 + q - 1 = 1 , then the mapping x * [ d1 , ...Page 287

On the other hand , Hölder's inequality ( III.3.2 )

On the other hand , Hölder's inequality ( III.3.2 )

**gives**1x * = | gle . Thus ( 0 * = \ gle The mapping x * → g is then a one - to - one isometric map of L ...### 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 | |

87 other sections not shown

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