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 A , and let do sup o ( po- p ) . The number do is finite , for if = DEA ...
... 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 A , and let do sup o ( po- p ) . The number do is finite , for if = DEA ...
Page 314
... sequentially com- pact if and only if there exists a non - negative μ in ba ( S , Σ ) such that uniformly for λεΚ . - lim λ ( E ) **** 0 μ ( E ) → 0 PROOF . Let KC ba ( S , 2 ) be weakly sequentially compact and let V UT be the ...
... sequentially com- pact if and only if there exists a non - negative μ in ba ( S , Σ ) such that uniformly for λεΚ . - lim λ ( E ) **** 0 μ ( E ) → 0 PROOF . Let KC ba ( S , 2 ) be weakly sequentially compact and let V UT be the ...
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
Preliminary Concepts | 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 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