Linear Operators: General theory |
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Page 40
... unit e , then an element x in R is called ( right , left ) regular in R in case R contains a ( right , left ) ... unit consists of the integers modulo 2 , i.e. , the two numbers 0 , 1. This Boolean ring , which we denote by P , is actually ...
... unit e , then an element x in R is called ( right , left ) regular in R in case R contains a ( right , left ) ... unit consists of the integers modulo 2 , i.e. , the two numbers 0 , 1. This Boolean ring , which we denote by P , is actually ...
Page 458
... unit sphere of Co contains no extremal points . 4 Let ( S , Σ , μ ) be a σ - finite positive measure space . Show that L1 ( S , E , ) is isometrically isomorphic to the conjugate X * of a B - space if and only if S can be written as a ...
... unit sphere of Co contains no extremal points . 4 Let ( S , Σ , μ ) be a σ - finite positive measure space . Show that L1 ( S , E , ) is isometrically isomorphic to the conjugate X * of a B - space if and only if S can be written as a ...
Page 485
... unit 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 ...
... unit 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 ...
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