Linear Operators: General theory |
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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 - + 1 + 3 < 2 * , k = 1 , 2 , . . . , and show that a Cauchy sequence in X can be chosen ...
... 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 - + 1 + 3 < 2 * , k = 1 , 2 , . . . , and show that a Cauchy sequence in X can be chosen ...
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 * 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 * is actually X ** - convergent , and that if Y is a separable B - space , then ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ