Linear Operators: General theory |
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Page 2
... union , or sum , of the sets a in A. This union is denoted by A or Ua . The intersection , or product , of the sets a in A is the set of α € A = = { a , b , . . . , c } bu ... Uc , and the all a in A which are elements of every a € A ...
... union , or sum , of the sets a in A. This union is denoted by A or Ua . The intersection , or product , of the sets a in A is the set of α € A = = { a , b , . . . , c } bu ... Uc , and the all a in A which are elements of every a € A ...
Page 10
... union of every one of its subfamilies , and the intersection of every one of its finite subfamilies . The pair ( X , 7 ) is called a topological space ; but sometimes ift is understood , we refer to X as a topological space . If τ , t1 ...
... union of every one of its subfamilies , and the intersection of every one of its finite subfamilies . The pair ( X , 7 ) is called a topological space ; but sometimes ift is understood , we refer to X as a topological space . If τ , t1 ...
Page 96
... union is in T. For an example of a finitely additive set function , let S = [ 0 , 1 ) and let be the family of intervals I = [ a , b ) , 0 ≤ a < b < 1 , with μ ( 1 ) = 7 b - a . - We will ordinarily require that the domain of an ...
... union is in T. For an example of a finitely additive set function , let S = [ 0 , 1 ) and let be the family of intervals I = [ a , b ) , 0 ≤ a < b < 1 , with μ ( 1 ) = 7 b - a . - We will ordinarily require that the domain of an ...
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 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 disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ