## Linear Operators: General theory |

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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 Ly , FCCC W CP .

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

not the ...

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 Ly , FCCC W CP .

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

not the ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

81 other sections not shown

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