## Linear Operators: General theory |

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Page 168

Let ( S , E , ) be a positive measure space and G a

Let ( S , E , ) be a positive measure space and G a

**separable**subset of Lp ( S , E , u , X ) , where 1 sp < 0. Then there is a set s , in E , a sub o ...Page 426

If X is

If X is

**separable**, let { xn } be a countable dense subset of X , and define | ( x * —y * ) xn | 0 ( 2 * , 4 * ) = Σ n = 1 21 1+ | ( 2 * —Y * ) xml It is ...Page 507

may be noted that the next theorem applies to every continuous linear map of L ( S , E , u ) into a

may be noted that the next theorem applies to every continuous linear map of L ( S , E , u ) into a

**separable**reflexive space . 10 THEOREM .### 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 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