Linear Operators: General theory |
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Page 40
... unit e , then an element æ 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 æ 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 41
... unit , then R / M is isomorphic with the field Ø . An important example of a Boolean ring with a unit is the ring of subsets of a fixed set . More precisely , let S be a set and let multiplica- tion and addition of arbitrary subsets E ...
... unit , then R / M is isomorphic with the field Ø . An important example of a Boolean ring with a unit is the ring of subsets of a fixed set . More precisely , let S be a set and let multiplica- tion and addition of arbitrary subsets E ...
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 , μ ) is isometrically isomorphic to the conjugate ** of a B - space X if and only if S can be written as ...
... 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 , μ ) is isometrically isomorphic to the conjugate ** of a B - space X if and only if S can be written as ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ