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Page 77
( 1 ) Emimn converges for every n ; ( 2 ) Enamn - hm , n + 1 ) converges for each m ; M ( 3 ) sup En 1 ( Amn - hm , n + 1 ) ] < 0o . M m = 0 ) The transformation preserves sums of series ( i.e. Σο ( Σοληλα , ) = no an ) if and only if ...
( 1 ) Emimn converges for every n ; ( 2 ) Enamn - hm , n + 1 ) converges for each m ; M ( 3 ) sup En 1 ( Amn - hm , n + 1 ) ] < 0o . M m = 0 ) The transformation preserves sums of series ( i.e. Σο ( Σοληλα , ) = no an ) if and only if ...
Page 145
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 ) < and such that { { n } converges uniformly on S- E. The sequence { { n } converges u ...
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 ) < and such that { { n } converges uniformly on S- E. The sequence { { n } converges u ...
Page 595
Let , fn be in F ( T ) , and let { f ( T ) / n ( T ) } converge to zero in the weak operator topology . ... converge for osm < aldo ) , and if limn + In ( 20 ) # 0 , then { fn ( T ) } converges in the weak operator topology .
Let , fn be in F ( T ) , and let { f ( T ) / n ( T ) } converge to zero in the weak operator topology . ... converge for osm < aldo ) , and if limn + In ( 20 ) # 0 , then { fn ( T ) } converges in the weak operator topology .
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
quences | 26 |
Copyright | |
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Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero