## Linear Operators: General theory |

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Page 77

( 1 ) Emamn

( 1 ) Emamn

**converges**for every n ; ( 2 ) Enlamn - am , n + 1**converges**for each m ; M ( 3 ) sup En E ( amnam , n + 1 ) | < 0 . M m = 0 ) The transformation preserves sums of series ( i.e. _o ( no āmnan ) = mo an ) if and only if the ...Page 145

A sequence of functions { n } defined on S with values in X

A sequence of functions { n } defined on S with values in X

**converges**u - uniformly if for each ε > 0 there is a set E € £ such that v ( u , E ) < E and such that { fn }**converges**uniformly on S- E. The sequence { fn }**converges**u ...Page 595

If each root 20 has finite order al20 ) , if the sequences { f4m ) ( 20 ) }

If each root 20 has finite order al20 ) , if the sequences { f4m ) ( 20 ) }

**converge**for o 5 m < ( 20 ) , and if limn + 1 ( 20 ) + 0 , then { fn ( T ) }**converges**in the weak operator topology . Moreover , X = f ) f ( T ) X © { x \ x e ...### 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