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 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 K1 and K2 . 12 COROLLARY . If K is a closed convex subset of a locally convex linear ...
... 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 K1 and K2 . 12 COROLLARY . If K is a closed convex subset of a locally convex linear ...
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 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ