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Page 458
... sphere of co contains no extremal points . 4 Let ( S , E , μ ) be a o - finite positive measure space . Show that L1 ( S , E , μ ) is isometrically isomorphic to the conjugate * of a B - space if and only if S can be written as a ...
... sphere of co contains no extremal points . 4 Let ( S , E , μ ) be a o - finite positive measure space . Show that L1 ( S , E , μ ) is isometrically isomorphic to the conjugate * of a B - space if and only if S can be written as a ...
Page 470
... sphere S of a B - space X into a conditionally compact subset of X , which sends the boundary { x || x | = 1 } into ... sphere of a reflexive B - space into itself always has a fixed point . Kakutani [ 5 ] gave an example to show that ...
... sphere S of a B - space X into a conditionally compact subset of X , which sends the boundary { x || x | = 1 } into ... sphere of a reflexive B - space into itself always has a fixed point . Kakutani [ 5 ] gave an example to show that ...
Page 485
... sphere S * of Y * is Y - compact ( V.4.2 ) , it follows from Lemma 7 and Lemma I.5.7 that T * S * is compact in the X ** topology of X * . Hence T * is weakly compact . Conversely , if T * is weakly compact , it follows from Lemma 7 ...
... sphere S * of Y * is Y - compact ( V.4.2 ) , it follows from Lemma 7 and Lemma I.5.7 that T * S * is compact in the X ** topology of X * . Hence T * is weakly compact . Conversely , if T * is weakly compact , it follows from Lemma 7 ...
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