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Page 72
... B - space ( or an F - space ) with the metric x + 3 = inf x + z . ze3 ( Hint : Given a Cauchy sequence in X / 3 , define a subsequence for which x - x + 1 + 3 ] < 2− * , k = 1 , 2 , ... , and show that a Cauchy sequence in X can be ...
... B - space ( or an F - space ) with the metric x + 3 = inf x + z . ze3 ( Hint : Given a Cauchy sequence in X / 3 , define a subsequence for which x - x + 1 + 3 ] < 2− * , k = 1 , 2 , ... , and show that a Cauchy sequence in X can be ...
Page 89
... B - algebras . Completion of spaces . In the definitions of F- and B - spaces , we required the spaces to be ... space satisfying properties ( i ) and ( ii ) of Definition 1.10 . Then X is isomorphic and isometric with a dense linear subspace ...
... B - algebras . Completion of spaces . In the definitions of F- and B - spaces , we required the spaces to be ... space satisfying properties ( i ) and ( ii ) of Definition 1.10 . Then X is isomorphic and isometric with a dense linear subspace ...
Page 398
... space . Let S be a Stone space and X C ( S ) the real continuous func- tions . Grothendieck [ 4 ; p . 168 ] showed that every X - convergent se- quence in X * is actually X ** - convergent , and that if Y is a separable B - space , then ...
... space . Let S be a Stone space and X C ( S ) the real continuous func- tions . Grothendieck [ 4 ; p . 168 ] showed that every X - convergent se- quence in X * is actually X ** - convergent , and that if Y is a separable B - space , then ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ