## Linear Operators: General theory |

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Page 168

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

Let ( S , Eu ) 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 - field Ey of E ( S ) , and a closed**separable**subspace X of X such that the ...Page 426

If X is

If X is

**separable**, let { xn } be a countable dense subset of X , and define ( x * — y * x , 0 , * ( 2 * y * ) = Σ n = 1 2 " 1 + 1 ( 2 * —- Y * ) x It is easy to verify that the topology of S * defined by this metric is weaker than the ...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 . Let ( S , E , u ) be a o - finite positive measure space , and let T be a weakly compact ...### 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