## 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 < 00. Then there is a set S , in E , a sub o - field of E ( S ) , and a closed**separable**subspace X of X such that the ...Page 501

If the compact Hausdorff space S has a countable base the space C ( S ) is

If the compact Hausdorff space S has a countable base the space C ( S ) is

**separable**. PROOF . By Theorems 1.6.19 and 1.6.12 , S is a**separable**metric space . If g ( x , y ) is a metric in S let fn ( x ) = g ( x , xn ) where { xm } is a ...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 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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