Linear Operators: General theory |
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Page 410
... 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 , ... , a be non - negative scalars with a , + ...
... 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 , ... , a be non - negative scalars with a , + ...
Page 418
... convex subsets of a locally convex linear topological space X , and if K1 is compact , then some non - zero continuous linear functional on X separates K , and K2 . 12 1 COROLLARY . If K is a closed convex subset of a locally convex ...
... convex subsets of a locally convex linear topological space X , and if K1 is compact , then some non - zero continuous linear functional on X separates K , and K2 . 12 1 COROLLARY . If K is a closed convex subset of a locally convex ...
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 ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz 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