## Linear Operators: General theory |

### From inside the book

Results 1-3 of 84

Page 8

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 ...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

We haven't found any reviews in the usual places.

### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

91 other sections not shown

### Other editions - View all

### Common terms and phrases

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