## Linear Operators: General theory |

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Page 39

Zorn's lemma ( 2.7 ) applies to give a maximal element in 8 , which is readily

Zorn's lemma ( 2.7 ) applies to give a maximal element in 8 , which is readily

**seen**to be a maximal right ideal containing lo . If I is a two - sided ideal in R , let x + I be defined as x + I { x + y \ y e I } .Page 254

Thus by forming the chain UB , Ugly ... , Ug's Vg , it is

Thus by forming the chain UB , Ugly ... , Ug's Vg , it is

**seen**that vg is equivalent to vg , and thus that , Ua UB UB VB is in V. Since { v } is a basis , the vector Wq has an expansion of the form ug = E ( Uq , VB ) V , Ee ( Ux ...Page 690

Pm , it is

Pm , it is

**seen**from Theorem 5.5 that n = nTп Pn rA ( r ) ( ) , s ) — ( 9 , 8 ) 0 n n almost everywhere on S and uniformly on the interval o srs 1 . The desired conclusion now follows from the identity ( vi ) and Theorem 5.5 .### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

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