## 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 of**subsets**of a set has the property that A € 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 CK is said to be an extremal**subset**of K if a proper convex combination ak ; + ( 1 - a ) ka , 0 < a < 1 , of two points of K is in A only if both kq and ...Page 440

totally ordered subfamily of A , the non - void set n A , is a closed extremal

totally ordered subfamily of A , the non - void set n A , is a closed extremal

**subset**of K which furnishes a lower bound for A 1. It follows by Zorn's lemma that A contains a minimal element A . Suppose that A , contains two distinct ...### 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