Linear Operators: General theory |
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Page 7
... belong to some subset E € E。, and x ≤ y in the ordering ≤ of that E 。. It is clear that if ( o , ≤ ' ) belongs to & it is an upper bound for &。. will now be shown that it is well - ordered and hence belongs to & . The statement xx ...
... belong to some subset E € E。, and x ≤ y in the ordering ≤ of that E 。. It is clear that if ( o , ≤ ' ) belongs to & it is an upper bound for &。. will now be shown that it is well - ordered and hence belongs to & . The statement xx ...
Page 35
... belongs to every subgroup of G ; and ( ab ) -1 = b - 1a - 1 . A mapping h : A → B between groups A and B is called a homo- morphism if h ( ab ) h ( a ) h ( b ) . A one - to - one homomorphism is called an isomorphism . If h : A → B is ...
... belongs to every subgroup of G ; and ( ab ) -1 = b - 1a - 1 . A mapping h : A → B between groups A and B is called a homo- morphism if h ( ab ) h ( a ) h ( b ) . A one - to - one homomorphism is called an isomorphism . If h : A → B is ...
Page 184
... belong to A1 . It follows that is closed under intersection and complementation and contains S. Thus is a field of sets . Moreover , each set of & belongs to D and hence PE . If the set function u is defined for Fe by the formula μ ( F ) ...
... belong to A1 . It follows that is closed under intersection and complementation and contains S. Thus is a field of sets . Moreover , each set of & belongs to D and hence PE . If the set function u is defined for Fe by the formula μ ( F ) ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ 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 ergodic exists f₁ finite dimensional function defined function f 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-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ