## Linear Operators: General theory |

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Page 335

Then L is complete and every

Then L is complete and every

**subset**A of L has a least upper bound which is the least upper bound of a countable**subset**of A. Proof . Let A be a**subset**of L which has an upper bound and let A , be the collection of least upper bounds of ...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 Ag . Suppose that A , contains two distinct ...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

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