Linear Operators: General theory |
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Page 103
... denote the class of functions equivalent to f ( i.e. all g such that f - g is a μ - null function ) , and let F ( S , E , μ , 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 f ( i.e. all g such that f - g is a μ - null function ) , and let F ( S , E , μ , 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 unit sphere in the space of variables a1 , ... , X¿ - 19 xi + 1 , ... , xn . Let at denote the positive square root { 1- ( x2 + ... + œ¿- 2 + x + 2 + ··· + x ) } 1/2 , and a denote the corresponding negative square root ; let p ...
... denote the unit sphere in the space of variables a1 , ... , X¿ - 19 xi + 1 , ... , xn . Let at denote the positive square root { 1- ( x2 + ... + œ¿- 2 + x + 2 + ··· + x ) } 1/2 , and a denote the corresponding negative square root ; let p ...
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