Linear Operators: General theory |
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Page 103
... denote the class of functions equivalent to ƒ ( i.e. all g such that f — g is a u - null function ) , and let F ( S , E , u , X ) denote the set of all such sets . f . If the following equations are used to define their left hand mem ...
... denote the class of functions equivalent to ƒ ( i.e. all g such that f — g is a u - null function ) , and let F ( S , E , u , X ) denote the set of all such sets . f . If the following equations are used to define their left hand mem ...
Page 142
... denote a set in 2 , the symbol M with or without subscripts will denote a set in for which v ( u , M ) = 0 , and N with or without subscripts will denote a subset of a set M. To see that the complement of a set EUN in E is also in E ...
... denote a set in 2 , the symbol M with or without subscripts will denote a set in for which v ( u , M ) = 0 , and N with or without subscripts will denote a subset of a set M. To see that the complement of a set EUN in E is also in E ...
Page 469
... Denote the determinant whose columns are the vectors få ( t ; x ) , fx ( t ; x ) by D。( t ; x ) and consider the ... denote the unit sphere in the space of variables x1 ,. Xi - 1 Xi + 1 , ... , xn . Let at denote the positive square ...
... Denote the determinant whose columns are the vectors få ( t ; x ) , fx ( t ; x ) by D。( t ; x ) and consider the ... denote the unit sphere in the space of variables x1 ,. Xi - 1 Xi + 1 , ... , xn . Let at denote the positive square ...
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