Linear Operators: General theory |
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Page 477
... operator topology is stronger than the weak 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 ...
... operator topology is stronger than the weak 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 ...
Page 511
... operator topology if and only if it is closed in the strong operator topology and Ax is conditionally compact for each xe X. 3 Let AC B ( X , Y ) . Then if A is compact in the weak operator topology , so is the weak operator closure of ...
... operator topology if and only if it is closed in the strong operator topology and Ax is conditionally compact for each xe X. 3 Let AC B ( X , Y ) . Then if A is compact in the weak operator topology , so is the weak operator closure of ...
Page 540
Nelson Dunford, Jacob T. Schwartz. operator and the operator mapping into a weakly complete space X. Weakly compact operators from C [ 0 , 1 ] to X were treated by Sirvint [ 3 ] . A very incisive discussion of weakly compact operators ...
Nelson Dunford, Jacob T. Schwartz. operator and the operator mapping into a weakly complete space X. Weakly compact operators from C [ 0 , 1 ] to X were treated by Sirvint [ 3 ] . A very incisive discussion of weakly compact operators ...
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 B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ