Linear Operators: General theory |
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Page 475
... topology and the weak , or X * , topology . If X is the conjugate space of Y , there is also the topology in X. The ... operator topologies , as given in the following definitions . 1 DEFINITION . The uniform operator topology in B ( X ...
... topology and the weak , or X * , topology . If X is the conjugate space of Y , there is also the topology in X. The ... operator topologies , as given in the following definitions . 1 DEFINITION . The uniform operator topology in B ( X ...
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 ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ