Linear Operators: General theory |
From inside the book
Results 1-3 of 73
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 41
... unit , then R / M is isomorphic with the field Ø2 . 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 Ø2 . 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 425
... unit sphere of X ** . It follows immediately that it contains every point in X ** . Q.E.D. Theorems 2 and 5 lead to an important result on reflexive spaces . 7 THEOREM . A B - space is reflexive if and only if its closed unit sphere is ...
... unit sphere of X ** . It follows immediately that it contains every point in X ** . Q.E.D. Theorems 2 and 5 lead to an important result on reflexive spaces . 7 THEOREM . A B - space is reflexive if and only if its closed unit sphere is ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
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 continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional 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 Russian 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