Linear Operators: General theory |
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Page 168
... separable subset of L , ( S , Z , μ , X ) , where 1 ≤ p < ∞ . Then there is a set S1 in 2 , a sub o - field Σ1 of Σ ( S1 ) , and a closed separable subspace X1 of X such that the restriction μ of μ to 2 has the following properties ...
... separable subset of L , ( S , Z , μ , X ) , where 1 ≤ p < ∞ . Then there is a set S1 in 2 , a sub o - field Σ1 of Σ ( S1 ) , and a closed separable subspace X1 of X such that the restriction μ of μ to 2 has the following properties ...
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 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