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 Y * 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 Y * 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
Preliminary Concepts | 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 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 ergodic exists f₁ finite dimensional function defined function f 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-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ