Linear Operators: General theory |
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Page 304
... positive measure space and let 1 ≤ p ≤ 0. Suppose f1 + f2 E - 18 , where fi , g are positive elements - k , in L , ( S , E , μ ) . Then there are positive elements hi in L2 ( S , Σ , μ ) , j = 1 , 2 , k = 1 , . . , n , such that n ...
... positive measure space and let 1 ≤ p ≤ 0. Suppose f1 + f2 E - 18 , where fi , g are positive elements - k , in L , ( S , E , μ ) . Then there are positive elements hi in L2 ( S , Σ , μ ) , j = 1 , 2 , k = 1 , . . , n , such that n ...
Page 305
... positive elements . Let f ; e L , ( S , 2 , μ ) , f¡ ≥ 0 , j Σ - 182 ; = 1 , 2 , and let f1 = 181 f2 = -182 ; be decompositions of f , and f2 into positive functions . Then Σg1i + Σg2 ; is a decomposition of fi + f2 and so To ( fi + f2 ) ...
... positive elements . Let f ; e L , ( S , 2 , μ ) , f¡ ≥ 0 , j Σ - 182 ; = 1 , 2 , and let f1 = 181 f2 = -182 ; be decompositions of f , and f2 into positive functions . Then Σg1i + Σg2 ; is a decomposition of fi + f2 and so To ( fi + f2 ) ...
Page 714
... positive measure space . Suppose that T is a positive linear operator in L1 ( S , E , μ ) such that Th / n converges to zero in the weak operator topology and let | T ” —K | < 1 for some positive integer n and some compact operator K ...
... positive measure space . Suppose that T is a positive linear operator in L1 ( S , E , μ ) such that Th / n converges to zero in the weak operator topology and let | T ” —K | < 1 for some positive integer n and some compact operator K ...
Contents
Preliminary Concepts | 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 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 ergodic exists f₁ finite dimensional function defined function f 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-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ