## Linear Operators: General theory |

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Page 8

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

= E for if x is in E but not in E , the ordering S ... 2 If a family & of

has the property that A € 8 if and only if every finite

...

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 , the ordering S ... 2 If a family & of

**subsets**of a sethas the property that A € 8 if and only if every finite

**subset**of A belongs to E , then...

Page 439

LAJIT UP DUAN LIVRAKIL . 8. Extremal Points 1 DEFINITION . Let K be a

of a real or complex linear vector space X. A non - void

an extremal

LAJIT UP DUAN LIVRAKIL . 8. Extremal Points 1 DEFINITION . Let K be a

**subset**of a real or complex linear vector space X. A non - void

**subset**A CK is said to bean extremal

**subset**of K if a proper convex combination akı + ( 1 - a ) ka , 0 ) < a ...Page 440

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

of K which furnishes a lower bound for A 1. It follows by Zorn's lemma that A

contains a minimal element Ao . Suppose that A , contains two distinct points p

and q ...

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 Ao . Suppose that A , contains two distinct points p

and q ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

81 other sections not shown

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