Linear Operators: General theory |
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Page 410
... convex subsets of the linear space X is convex . As examples of convex subsets of X , we note the subspaces of X , and the subsets of X consisting of one point . .... 3 LEMMA . Let x1 , · an be points in the convex set K and let a1 ...
... convex subsets of the linear space X is convex . As examples of convex subsets of X , we note the subspaces of X , and the subsets of X consisting of one point . .... 3 LEMMA . Let x1 , · an be points in the convex set K and let a1 ...
Page 461
... convex set K which is compact in the X * topology of the normed linear space X , can be separated from an arbitrary closed convex set disjoint from K ( com- pare Theorem 2.10 ) . Tukey observed that this result implies that in a ...
... convex set K which is compact in the X * topology of the normed linear space X , can be separated from an arbitrary closed convex set disjoint from K ( com- pare Theorem 2.10 ) . Tukey observed that this result implies that in a ...
Page 842
... Convex combination , V.2.2 ( 414 ) . See also Convex hull , Convex set , Convex space ) Convex function , definition , VI.10.1 ( 520 ) study of , VI.10 Convex hull , V.2.2 ( 414 ) Convex set , II.4.1 ( 70 ) definition , V.1.1 ( 410 ) ...
... Convex combination , V.2.2 ( 414 ) . See also Convex hull , Convex set , Convex space ) Convex function , definition , VI.10.1 ( 520 ) study of , VI.10 Convex hull , V.2.2 ( 414 ) Convex set , II.4.1 ( 70 ) definition , V.1.1 ( 410 ) ...
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 continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional 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 Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ