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 ,. ... , xn 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 ,. ... , xn 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 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