Linear Operators: General theory |
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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 rca ( 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 rca ( 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 xe X. 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 xe X. 3 Let AC B ( X , Y ) . Then if A is compact in the weak operator topology , so is the weak operator closure of ...
Page 540
Nelson Dunford, Jacob T. Schwartz. operator and the operator mapping into a weakly complete space X. Weakly compact operators from C [ 0 , 1 ] to X were treated by Sirvint [ 3 ] . A very incisive discussion of weakly compact operators ...
Nelson Dunford, Jacob T. Schwartz. operator and the operator mapping into a weakly complete space X. Weakly compact operators from C [ 0 , 1 ] to X were treated by Sirvint [ 3 ] . A very incisive discussion of weakly compact operators ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space 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 exists f₁ finite dimensional function defined function f g₁ 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-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ