Linear Operators: General theory |
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Page 430
... Weak Topologies . Weak Compactness We have already introduced and employed the concepts of weak sequential compactness ( II.3.25 ) and compactness in the X * ( or weak ) topology . There is at least one other type of weak compactness ...
... Weak Topologies . Weak Compactness We have already introduced and employed the concepts of weak sequential compactness ( II.3.25 ) and compactness in the X * ( or weak ) topology . There is at least one other type of weak compactness ...
Page 477
... 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 ( X , Y ) . 4 THEOREM . A linear ...
... 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 ( X , Y ) . 4 THEOREM . A linear ...
Page 511
... weak operator topology is that where each factor is taken to have the * topology . 2 A set AC B ( X , Y ) is compact in the weak operator topology if and only if it is closed in the weak operator topology and the weak closure of Ax is ...
... weak operator topology is that where each factor is taken to have the * topology . 2 A set AC B ( X , Y ) is compact in the weak operator topology if and only if it is closed in the weak operator topology and the weak closure of Ax is ...
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