Linear Operators: General theory |
From inside the book
Results 1-3 of 68
Page 140
... intervals . An interval is finite if both its end points are finite ; otherwise it is an infinite interval . If ƒ is a complex function on an interval I , the total variation of f on I is defined by the equation v ( f , I ) * n sup Σ ...
... intervals . An interval is finite if both its end points are finite ; otherwise it is an infinite interval . If ƒ is a complex function on an interval I , the total variation of f on I is defined by the equation v ( f , I ) * n sup Σ ...
Page 141
... interval I = ( a , b ) which may be finite or infinite . It is assumed that ( i ) f ( s ) = lim f ( s + ) , 0 < -3 se I ; i.e. , f is continuous on the right at every point in the open interval I. The closed interval Ī = [ a , b ] is a ...
... interval I = ( a , b ) which may be finite or infinite . It is assumed that ( i ) f ( s ) = lim f ( s + ) , 0 < -3 se I ; i.e. , f is continuous on the right at every point in the open interval I. The closed interval Ī = [ a , b ] is a ...
Page 283
... interval 1. By the same rea- soning , contains a subsequence { f } convergent uniformly on the interval 2. In this way successive subsequences are chosen so that the limit lim , fn , ( x ) exists uniformly on the interval a≤n . The ...
... interval 1. By the same rea- soning , contains a subsequence { f } convergent uniformly on the interval 2. In this way successive subsequences are chosen so that the limit lim , fn , ( x ) exists uniformly on the interval a≤n . The ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
59 other sections not shown
Other editions - View all
Common terms and phrases
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