Linear Operators: General theory |
From inside the book
Results 1-3 of 61
Page 168
... separable subset of L ( S , Σ , u , X ) , where 1 ≤ p < ∞o . Then there is a set S1 in Σ , a sub o - field Σ1 of Σ ( S1 ) , and a closed separable subspace X of X such that the restriction μ of μ to has the following properties : ( i ) ...
... separable subset of L ( S , Σ , u , X ) , where 1 ≤ p < ∞o . Then there is a set S1 in Σ , a sub o - field Σ1 of Σ ( S1 ) , and a closed separable subspace X of X such that the restriction μ of μ to has the following properties : ( i ) ...
Page 501
... separable . Q.E.D. Let U be the closed unit sphere in L1 ( S , E , μ ) . Then , by the pre- ceding lemma , since K = TU is compact and has a countable base the space C ( K ) is separable . Since a subspace of a separable metric space is ...
... separable . Q.E.D. Let U be the closed unit sphere in L1 ( S , E , μ ) . Then , by the pre- ceding lemma , since K = TU is compact and has a countable base the space C ( K ) is separable . Since a subspace of a separable metric space is ...
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 , E , u ) . 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 , E , u ) . If T is weakly compact and has a ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ