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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 512
... weak operator topology if and only if à is compact in the weak operator topology . 6 If is reflexive , then the closed unit sphere of B ( X , Y ) is compact in the weak operator topology . Conversely , if the closed unit . sphere of B ...
... weak operator topology if and only if à is compact in the weak operator topology . 6 If is reflexive , then the closed unit sphere of B ( X , Y ) is compact in the weak operator topology . Conversely , if the closed unit . sphere of B ...
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
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ