Linear Operators: General theory |
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Page 511
... topology of operators in B ( X , Y ) is identical with the usual product topology where the strong topology is taken in each Y , and that the weak operator topology is that where each factor is taken to have the * topology . 2 A set AC ...
... topology of operators in B ( X , Y ) is identical with the usual product topology where the strong topology is taken in each Y , and that the weak operator topology is that where each factor is taken to have the * topology . 2 A set AC ...
Page 512
... operator topology . Conversely , if the closed unit sphere of B ( X , Y ) is compact in the weak operator topology , Y is reflexive . 7 Define the BWO topology for B ( X , Y ) to be the strongest topology which coincides with the weak ...
... operator topology . Conversely , if the closed unit sphere of B ( X , Y ) is compact in the weak operator topology , Y is reflexive . 7 Define the BWO topology for B ( X , Y ) to be the strongest topology which coincides with the weak ...
Page 599
... operator topology , and ( b ) , the space X can be written as a direct sum X = X1 → X2 , where TnX2 ≤ X2 for all n ≥ 1. ( Hint . Show first that the sequence { T } has one and only one accumulation point in the weak operator topology ...
... operator topology , and ( b ) , the space X can be written as a direct sum X = X1 → X2 , where TnX2 ≤ X2 for all n ≥ 1. ( Hint . Show first that the sequence { T } has one and only one accumulation point in the weak operator topology ...
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 converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ 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-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ