Linear Operators: General theory |
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Page 168
... separable subset of L , ( S , E , μ , X ) , where 1 ≤ p < ∞ . Then there is a set S1 in Σ , a sub o - field Σ1 of Σ ( §1 ) , and a closed separable subspace X1 of such that the restriction μ of μ to Σ has the following properties ...
... separable subset of L , ( S , E , μ , X ) , where 1 ≤ p < ∞ . Then there is a set S1 in Σ , a sub o - field Σ1 of Σ ( §1 ) , and a closed separable subspace X1 of such that the restriction μ of μ to Σ has the following properties ...
Page 426
... separable , let { n } be a countable dense subset of X , and define 00 Q ( x * , y * ) = Σ n = 1 1 | ( x * —y * ) xn ... separable , and from Corollary II.3.13 that X1 = X. Q.E.D. - 2 THEOREM . If X is a B - space , then the X * topology ...
... separable , let { n } be a countable dense subset of X , and define 00 Q ( x * , y * ) = Σ n = 1 1 | ( x * —y * ) xn ... separable , and from Corollary II.3.13 that X1 = X. Q.E.D. - 2 THEOREM . If X is a B - space , then the X * topology ...
Page 854
... Separability and embedding , V.7.12 ( 436 ) , V.7.14 ( 436 ) Separability and metrizability , V.5.1-2 ( 426 ) Separable sets , 1.6.11 ( 21 ) . ( See also Separable linear manifolds ) Separable linear manifolds , II.1.5 ( 50 ) . ( See also ...
... Separability and embedding , V.7.12 ( 436 ) , V.7.14 ( 436 ) Separability and metrizability , V.5.1-2 ( 426 ) Separable sets , 1.6.11 ( 21 ) . ( See also Separable linear manifolds ) Separable linear manifolds , II.1.5 ( 50 ) . ( See also ...
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 ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ