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Page 72
1.11 ) is a B - space ( or an F - space ) with the metric ( x + 3 ) = inf ( x + 2 !. ze3 ( Hint : Given a Cauchy sequence in X / 3 , define a subsequence for which ** —Xx + 1 + 31 < 2- , k = 1 , 2 , . . . , and show that a Cauchy ...
1.11 ) is a B - space ( or an F - space ) with the metric ( x + 3 ) = inf ( x + 2 !. ze3 ( Hint : Given a Cauchy sequence in X / 3 , define a subsequence for which ** —Xx + 1 + 31 < 2- , k = 1 , 2 , . . . , and show that a Cauchy ...
Page 89
In the definitions of F- and B - spaces , we required the spaces to be complete in their metric topology . Occasionally it is necessary to consider ... Let X be a linear space satisfying properties ( i ) and ( ii ) of Definition 1.10 .
In the definitions of F- and B - spaces , we required the spaces to be complete in their metric topology . Occasionally it is necessary to consider ... Let X be a linear space satisfying properties ( i ) and ( ii ) of Definition 1.10 .
Page 398
168 ] showed that every X - convergent sequence in X * is actually X ** - convergent , and that if Y is a separable B - space , then any operator in B ( X , Y ) is weakly compact . Goodner [ 1 ; p . 103 ] proved that the unit sphere in ...
168 ] showed that every X - convergent sequence in X * is actually X ** - convergent , and that if Y is a separable B - space , then any operator in B ( X , Y ) is weakly compact . Goodner [ 1 ; p . 103 ] proved that the unit sphere in ...
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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