## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 89

Page 8

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

E for if a. is in E but not in Eo the ordering so ... 2 If a family & of

has the property that A e & if and only if every finite

...

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

**subset**Eo of E. Now Eo =E for if a. is in E but not in Eo the ordering so ... 2 If a family & of

**subsets**of a sethas the property that A e & if and only if every finite

**subset**of A belongs to 6, then...

Page 440

totally ordered subfamily of .2/, the non-void set O.2/, is a closed extremal

of K which furnishes a lower bound for ...'. It follows by Zorn's lemma that .2/

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

and q.

totally ordered subfamily of .2/, the non-void set O.2/, is a closed extremal

**subset**of K which furnishes a lower bound for ...'. It follows by Zorn's lemma that .2/

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

and q.

Page 456

(Schauder-Tychonoff) A compact conver

topological space has the fired point property. PRoof. By Zorn's lemma there

exists a minimal convex

previous ...

(Schauder-Tychonoff) A compact conver

**subset**of a locally conver lineartopological space has the fired point property. PRoof. By Zorn's lemma there

exists a minimal convex

**subset**Kı of K with the property that TK C K1. By theprevious ...

### What people are saying - Write a review

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

### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

27 other sections not shown

### Common terms and phrases

additive set function algebra Amer analytic arbitrary B-space Banach baſs Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complete complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense differential Doklady Akad element equation equivalent exists finite dimensional function defined function f g-field g-finite Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure Lemma Let f lim ſº linear map linear operator linear topological space Lp(S Math measurable functions measure space metric space Nauk SSSR N.S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc properties proved real numbers Riesz scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact zero