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 g ( Po P ) . The number do is finite , for if 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 g ( Po P ) . The number do is finite , for if e ...
Page 314
... sequentially com- pact if and only if there exists a non - negative μ in ba ( S , E ) such that lim λ ( E ) = 0 μ ( E ) → 0 uniformly for λε Κ . PROOF . Let KC ba ( S , E ) be weakly sequentially compact and let V = UT be the isometric ...
... sequentially com- pact if and only if there exists a non - negative μ in ba ( S , E ) such that lim λ ( E ) = 0 μ ( E ) → 0 uniformly for λε Κ . PROOF . Let KC ba ( S , E ) be weakly sequentially compact and let V = UT 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
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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 disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ