## Linear Operators: General theory |

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Results 1-3 of 88

Page 8

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

E for if x is in E but not in E0 the ordering :g0 in E0 may be extended to the set E0[

j{x} by defining y ^0x for y € £„. Q.E.D. 3. Exercises 1 If (E, 5S) is a p.o.s. with the ...

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

**subset**E0 of E. Now E0 =E for if x is in E but not in E0 the ordering :g0 in E0 may be extended to the set E0[

j{x} by defining y ^0x for y € £„. Q.E.D. 3. Exercises 1 If (E, 5S) is a p.o.s. with the ...

Page 439

8. Extremal Points 1 Definition. Let K be a

vector space 3c. A non-void

proper convex combination ^ + (1— a)^, 0 < a < 1, of two points of AT is in A only

if ...

8. Extremal Points 1 Definition. Let K be a

**subset**of a real or complex linearvector space 3c. A non-void

**subset**A Q K is said to be an extremal**subset**of K if aproper convex combination ^ + (1— a)^, 0 < a < 1, of two points of AT is in A only

if ...

Page 440

totally ordered subfamily of si, the non-void set Ds/1 is a closed extremal

of K which furnishes a lower bound for s/v It follows by Zorn's lemma that si

contains a minimal element A0. Suppose that A0 contains two distinct points p

and q.

totally ordered subfamily of si, the non-void set Ds/1 is a closed extremal

**subset**of K which furnishes a lower bound for s/v It follows by Zorn's lemma that si

contains a minimal element A0. Suppose that A0 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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