Linear Operators: General theory |
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Page 22
... sequentially compact . Conversely , suppose that A is sequentially compact and closed . It will first be shown that A is separable . Let po be an arbitrary point of 4 , and let do sup ( Po , P ) . The number do is finite , for if DEA e ...
... sequentially compact . Conversely , suppose that A is sequentially compact and closed . It will first be shown that A is separable . Let po be an arbitrary point of 4 , and let do sup ( Po , P ) . The number do is finite , for if DEA e ...
Page 314
... sequentially com- pact if and only if there exists a non - negative u in ba ( S , E ) such that 12 uniformly for λε Κ . lim λ ( E ) = 0 μ ( E ) -0 PROOF . Let KC ba ( S , E ) be weakly sequentially compact and let VUT be the isometric ...
... sequentially com- pact if and only if there exists a non - negative u in ba ( S , E ) such that 12 uniformly for λε Κ . lim λ ( E ) = 0 μ ( E ) -0 PROOF . Let KC ba ( S , E ) be weakly sequentially compact and let VUT be the isometric ...
Page 511
... compact in the weak operator topology if and only if it is closed in the weak operator topology and the weak closure ... sequentially compact in the weak operator topology , its weak operator closure is compact in the weak operator ...
... compact in the weak operator topology if and only if it is closed in the weak operator topology and the weak closure ... sequentially compact in the weak operator topology , its weak operator closure is compact in the weak operator ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
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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