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 541
Nelson Dunford, Jacob T. Schwartz. compact and compact operators from L ( S ) to an arbitrary space X. Phillips [ 3 ] treated the same case for an arbitrary o - finite measure space obtaining a representation of the general operator as ...
Nelson Dunford, Jacob T. Schwartz. compact and compact operators from L ( S ) to an arbitrary space X. Phillips [ 3 ] treated the same case for an arbitrary o - finite measure space obtaining a representation of the general operator as ...
Page 577
... Compact Operators It has been observed in some of the exercises in Section VI.9 that a number of linear operators of importance in analysis either are com- pact , or have compact squares . The structure of the spectrum of such an operator ...
... Compact Operators It has been observed in some of the exercises in Section VI.9 that a number of linear operators of importance in analysis either are com- pact , or have compact squares . The structure of the spectrum of such an operator ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
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 closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism 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 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ