Linear Operators: General theory |
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Page 67
... reflexive B - space is reflexive . = PROOF . Let be a closed linear manifold in the reflexive space X. Let : x * y * be defined by the equation ( x * ) y x * y , ye Y. Clear- ly | § ( x * ) | ≤ | x * | , so that § : X * → Y * . Let ŋ ...
... reflexive B - space is reflexive . = PROOF . Let be a closed linear manifold in the reflexive space X. Let : x * y * be defined by the equation ( x * ) y x * y , ye Y. Clear- ly | § ( x * ) | ≤ | x * | , so that § : X * → Y * . Let ŋ ...
Page 88
... reflexive . Examples of reflexive B - spaces are given in Chapter IV , and a necessary and sufficient condition for reflexivity is given in Theorem V.4.7 . It is a consequence of Theorem V.6.1 that a necessary and sufficient condition ...
... reflexive . Examples of reflexive B - spaces are given in Chapter IV , and a necessary and sufficient condition for reflexivity is given in Theorem V.4.7 . It is a consequence of Theorem V.6.1 that a necessary and sufficient condition ...
Page 512
... reflexive . 7 Define the BWO topology for B ( X , Y ) to be the strongest topology which coincides with the weak ... reflexive then a fundamental set of neighborhoods of zero in the BWO topology is given by the sets { T \ T e B ( X , Y ) ...
... reflexive . 7 Define the BWO topology for B ( X , Y ) to be the strongest topology which coincides with the weak ... reflexive then a fundamental set of neighborhoods of zero in the BWO topology is given by the sets { T \ T e B ( X , Y ) ...
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