Linear Operators: General theory |
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Page 4
... denotes the infimum of all numbers b with the property that only a finite set of numbers in A exceed b ; the de- finition of ... denote the least upper bound of F by sup F or lub F and the greatest lower bound of F by inf F or glb F. 4 ...
... denotes the infimum of all numbers b with the property that only a finite set of numbers in A exceed b ; the de- finition of ... denote the least upper bound of F by sup F or lub F and the greatest lower bound of F by inf F or glb F. 4 ...
Page 103
... denote the class of functions equivalent to f ( 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 f ( 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 * is also in 2 ...
... 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 * is also in 2 ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ