## Linear Operators: General theory |

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Page 7

Thus it has been

Thus it has been

**shown**that E , has an upper bound . Hence , by Theorem 7 , there is a maximal I.2.8 7 PARTIALLY ORDERED SYSTEMS Partially Ordered Systems.Page 335

It will first be

It will first be

**shown**that W satisfies the hypothesis of Zorn's lemma . To do this we let W , be a totally ordered subset of W ( 1.22 ) and let c CUW .Page 553

841 ] has

841 ] has

**shown**that in Hilbert space C is a maximal two - sided ideal . We have seen in Theorems 7.4 and 8.12 that in the spaces C and Ly , FCCC W CP .### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

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Acad 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 semi-group 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