Linear Operators: General theory |
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Page 414
... convex set K has at least one interior point p , an internal point q is an interior point , and a boundary point q , is a bounding point . Since q is internal , the vector rep + ( 1 + ε ) q , belongs to K for some sufficiently small ...
... convex set K has at least one interior point p , an internal point q is an interior point , and a boundary point q , is a bounding point . Since q is internal , the vector rep + ( 1 + ε ) q , belongs to K for some sufficiently small ...
Page 461
... convex set disjoint from K ( com- pare Theorem 2.10 ) . Tukey observed that this 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 ...
... convex set disjoint from K ( com- pare Theorem 2.10 ) . Tukey observed that this 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 ...
Page 842
... 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 ) study of , V.1-2 Convex space , locally , V.2.9 ...
... 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 ) study of , V.1-2 Convex space , locally , V.2.9 ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ