## Linear Operators: General theory |

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Page 168

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

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

**separable**subset of L , ( S , E , u , X ) , where 1 sp < 0o . Then there is a set S , in E , a sub o - field Ey of E ( S ) , and a closed**separable**subspace X , of 2 such that the ...Page 426

If X is

If X is

**separable**, let { xn } be a countable dense subset of X , and define 1 | ( x * —y * ) xm | 8 ( 2 * , y * ) n = 1 21 1 + ( x * -- ** ) x It is easy to verify that the topology of S * defined by this metric is weaker than the X ...Page 504

Theorem 6 remains valid if the hypothesis that X * is the conjugate space of a

Theorem 6 remains valid if the hypothesis that X * is the conjugate space of a

**separable**space is replaced by the hypothesis that X * is the conjugate space of an arbitrary B - space and T has a**separable**range .### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero