Linear Operators: General theory |
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Page 40
... unit e , then an element a 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 P2 , is ...
... unit e , then an element a 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 P2 , is ...
Page 458
... unit sphere of c 。 contains no extremal points . 4 Let ( S , 2 , μ ) be a σ - 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 ...
... unit sphere of c 。 contains no extremal points . 4 Let ( S , 2 , μ ) be a σ - 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 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
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality 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 o-field 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 theory topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ