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 S in 2 , a sub o - field Σ1 of Σ ( S1 ) , and a closed separable subspace X of such that the restriction μ of μ to 2 has the following properties : ( i ) ...
... separable subset of L ( S , E , μ , X ) , where 1 ≤ p < ∞ . Then there is a set S in 2 , a sub o - field Σ1 of Σ ( S1 ) , and a closed separable subspace X of such that the restriction μ of μ to 2 has the following properties : ( i ) ...
Page 507
... separable sub- set of the B - space X. Then there exists a μ - essentially unique bounded measurable function x ... separable range . PROOF . Let U be the closed unit sphere of L1 ( S , Σ , μ ) . If T is weakly compact and has a ...
... separable sub- set of the B - space X. Then there exists a μ - essentially unique bounded measurable function x ... separable range . PROOF . Let U be the closed unit sphere of L1 ( S , Σ , μ ) . If T is weakly compact and has a ...
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 continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional 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 Russian 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