## Linear Operators: General theory |

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Hence , by Theorem 7 , there is a maximal well - ordered

Hence , by Theorem 7 , there is a maximal well - ordered

**subset**E. of E. Now E. = E for if x is in E but not in E ... 2 If a family E of**subsets**of a set has the property that AC E if and only if every finite**subset**of A belongs to E ...Page 439

Let K be a

Let K be a

**subset**of a real or complex linear vector space X. A non - void**subset**A C K is said to be an extremal**subset**of K if a proper convex combination ak ; + ( 1 - a ) k2 , 0 ) < a < 1 , of two points of K is in A only if both k ...Page 456

( Schauder - Tychonoff ) A compact convex

( Schauder - Tychonoff ) A compact convex

**subset**of a locally convex linear topological space has the fixed point property . Proof . By Zorn's lemma there exists a minimal convex**subset**K , of K with the property that TK , CK .### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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