Linear Operators: General theory |
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Page 388
... results to a certain class of functions closely related to L1 , but which do not form a B - space . The reader is referred to his paper for the details . Corollary 8.13 is a classical result due to Schur [ 1 ] . There is a similar ...
... results to a certain class of functions closely related to L1 , but which do not form a B - space . The reader is referred to his paper for the details . Corollary 8.13 is a classical result due to Schur [ 1 ] . There is a similar ...
Page 390
... result is proved . ( For other results related to the atomic struc- ture of a measure space , see Hahn and Rosenthal [ 1 ; pp.45–53 ] and Halmos [ 5 ; pp . 165-174 ] . ) Theorem 9.14 is due to Bochner [ 3 ] . Bochner and Phillips [ 1 ] ...
... result is proved . ( For other results related to the atomic struc- ture of a measure space , see Hahn and Rosenthal [ 1 ; pp.45–53 ] and Halmos [ 5 ; pp . 165-174 ] . ) Theorem 9.14 is due to Bochner [ 3 ] . Bochner and Phillips [ 1 ] ...
Page 461
... result implies that in a reflexive B - space two disjoint closed convex sets , one of which is bounded , can be separated by a hyperplane . Tukey demonstrated that these results cannot be extended very far by giving examples of : ( i ) ...
... result implies that in a reflexive B - space two disjoint closed convex sets , one of which is bounded , can be separated by a hyperplane . Tukey demonstrated that these results cannot be extended very far by giving examples of : ( i ) ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ 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 ergodic exists f₁ finite dimensional function defined function f 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-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ