## Linear Operators: General theory |

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... 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 ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

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