Linear Operators: General theory |
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Page 494
... compact operator . Q.E.D. 4 THEOREM . If T is a weakly compact operator from C ( S ) to X , then T sends weak Cauchy sequences into strongly convergent sequences . Consequently , T maps conditionally weakly compact subsets of C ( S ) ...
... compact operator . Q.E.D. 4 THEOREM . If T is a weakly compact operator from C ( S ) to X , then T sends weak Cauchy sequences into strongly convergent sequences . Consequently , T maps conditionally weakly compact subsets of C ( S ) ...
Page 539
Nelson Dunford, Jacob T. Schwartz. operator and its importance was clearly recognized by E. Schmidt [ 1 ] , to whom the geometrical terminology in linear space theory is due . Compact and weakly compact operators . The concept of a compact ...
Nelson Dunford, Jacob T. Schwartz. operator and its importance was clearly recognized by E. Schmidt [ 1 ] , to whom the geometrical terminology in linear space theory is due . Compact and weakly compact operators . The concept of a compact ...
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