## Linear Operators: General theory |

### From inside the book

Results 1-3 of 83

Page 7

... where x s'y , whenever x and y both belong to some subset E , E En , and x Soy

in the ordering Fo of that En . It is clear that if ( UE , S ' ) belongs to & it is an upper

bound for E. It will now be

... where x s'y , whenever x and y both belong to some subset E , E En , and x Soy

in the ordering Fo of that En . It is clear that if ( UE , S ' ) belongs to & it is an upper

bound for E. It will now be

**shown**that it is well - ordered and hence belongs to ...Page 335

It will first be

we let W , be a totally ordered subset of W ( 1.22 ) and let c CUW .. Then , for

some a € Wo , cna is not void . Let x be the smallest element of coa and let y be

any ...

It will first be

**shown**that W satisfies the hypothesis of Zorn's lemma . To do thiswe let W , be a totally ordered subset of W ( 1.22 ) and let c CUW .. Then , for

some a € Wo , cna is not void . Let x be the smallest element of coa and let y be

any ...

Page 553

841 ] has

seen in Theorems 7 . 4 and 8 . 12 that in the spaces C and Li , FCCC W CP .

Grothendieck [ 4 ; p . 153 ] proved that in C , the ideals W and P coincide . This is

not ...

841 ] has

**shown**that in Hilbert space C is a maximal two - sided ideal . We haveseen in Theorems 7 . 4 and 8 . 12 that in the spaces C and Li , FCCC W CP .

Grothendieck [ 4 ; p . 153 ] proved that in C , the ideals W and P coincide . This is

not ...

### What people are saying - Write a review

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

### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

### Other editions - View all

### Common terms and phrases

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