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 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 ...
Page 858
... Weak limit , definition , II.3.25 ( 67 ) Weak sequential compactness , defini- tion , II.3.25 ( 67 ) in reflexive spaces , II.3.28 ( 68 ) in special spaces , IV.15 Weak topology in a B - space , ( 419 ) bounded topology in X * , V.5.3 ...
... Weak limit , definition , II.3.25 ( 67 ) Weak sequential compactness , defini- tion , II.3.25 ( 67 ) in reflexive spaces , II.3.28 ( 68 ) in special spaces , IV.15 Weak topology in a B - space , ( 419 ) bounded topology in X * , V.5.3 ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ