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
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
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 compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality 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 o-field 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 theory topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ