Linear Operators: General theory |
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Page 477
... operator topology is stronger than the weak operator topology . With its uniform operator topology , B ( X , Y ) becomes a B - space ; as such , it has a weak topology which should not be confused with the weak operator topology in B ...
... operator topology is stronger than the weak operator topology . With its uniform operator topology , B ( X , Y ) becomes a B - space ; as such , it has a weak topology which should not be confused with the weak operator topology in B ...
Page 494
... operator T , defined by ( b ) , is a bounded linear operator on C ( S ) to X whose adjoint T * is given by ( d ) . From IV.10.2 we conclude that T * maps the unit sphere of X * into a conditionally weakly compact set of rea ( S ) , and ...
... operator T , defined by ( b ) , is a bounded linear operator on C ( S ) to X whose adjoint T * is given by ( d ) . From IV.10.2 we conclude that T * maps the unit sphere of X * into a conditionally weakly compact set of rea ( S ) , and ...
Page 511
... operator topology if and only if it is closed in the strong operator topology and Ax is conditionally compact for each a ex . 3 Let AC B ( X , Y ) . Then if A is compact in the weak operator topology , so is the weak operator closure of ...
... operator topology if and only if it is closed in the strong operator topology and Ax is conditionally compact for each a ex . 3 Let AC B ( X , Y ) . Then if A is compact in the weak operator topology , so is the weak operator closure of ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
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 Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ