## Linear Operators: General theory |

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

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

property that A e E 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 ... 2 If a family E of

**subsets**of a set has theproperty that A e E if and only if every finite

**subset**of A belongs to E , then E ...Page 439

Let K be a

A C K is said to be an extremal

1 - a ) k , , 0 ) < a < 1 , of two points of K is in A only if both ky and kq are in 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 ) k , , 0 ) < a < 1 , of two points of K is in A only if both ky and kq are in A ...

Page 440

totally ordered subfamily of A , the non - void set 0 A , is a closed extremal

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

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

and q ...

totally ordered subfamily of A , the non - void set 0 A , is a closed extremal

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

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

and q ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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