## Linear Operators: General theory |

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Page 410

A set K CX is

A set K CX is

**convex**if x , y eK , and 0 sa şi , imply ax + ( 1 - a ) y e K. The following lemma is an obvious consequence of Definition 1 . 2 LEMMA .Page 418

If Ky , K , are disjoint closed ,

If Ky , K , are disjoint closed ,

**convex**subsets of a locally**convex**linear topological space X , and if K , is compact , then some non - zero continuous ...Page 461

and an arbitrary

and an arbitrary

**convex**set is possible , provided they are disjoint ( compare Theorem 2.8 ) . He also proved that a**convex**set K which is compact in the X ...### 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