Linear Operators: General theory |
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Page 304
... positive measure space and let 1 ≤ p ≤ ∞o . Suppose f1 + f2 = -18 , where fi , gx are positive elements k = 1 in L „ ( S , Σ , μ ) . Then there are positive elements h ̧ in L ( S , Σ , μ ) , j = 1 , 2 , k * 1 , .. n , such that n な ...
... positive measure space and let 1 ≤ p ≤ ∞o . Suppose f1 + f2 = -18 , where fi , gx are positive elements k = 1 in L „ ( S , Σ , μ ) . Then there are positive elements h ̧ in L ( S , Σ , μ ) , j = 1 , 2 , k * 1 , .. n , such that n な ...
Page 305
... positive elements . Let f , e L , ( S , Σ , μ ) , f ; ≥ 0 , j 1 , 2 , -181i , f2 = -182 ; be decompositions of ƒ1 and ƒ1⁄2 into fi positive functions . Then Σgii + Σg2 ; is a decomposition of ƒ1 + ƒ1⁄2 , and let f1 = and so To ( f1 + ...
... positive elements . Let f , e L , ( S , Σ , μ ) , f ; ≥ 0 , j 1 , 2 , -181i , f2 = -182 ; be decompositions of ƒ1 and ƒ1⁄2 into fi positive functions . Then Σgii + Σg2 ; is a decomposition of ƒ1 + ƒ1⁄2 , and let f1 = and so To ( f1 + ...
Page 714
... positive measure space . Suppose that T is a positive linear operator in L1 ( S , E , μ ) such that Tn converges to zero in the weak operator topology and let | T " -K | < 1 for some positive integer n and some compact operator K. Then ...
... positive measure space . Suppose that T is a positive linear operator in L1 ( S , E , μ ) such that Tn converges to zero in the weak operator topology and let | T " -K | < 1 for some positive integer n and some compact operator K. Then ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ