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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 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 ...
Page 541
Nelson Dunford, Jacob T. Schwartz. compact and compact operators from L1 ( 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 L1 ( 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 ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ