Linear Operators: General theory |
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Page 477
... operator topology . With its uniform operator topology , B ( X , Y ) becomes a B - space ; as such , it has a weak topology which should not be confused with the weak operator topology in B ( X , Y ) . 4 THEOREM . A linear functional on ...
... operator topology . With its uniform operator topology , B ( X , Y ) becomes a B - space ; as such , it has a weak topology which should not be confused with the weak operator topology in B ( X , Y ) . 4 THEOREM . A linear functional on ...
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
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