On approximation numbers of composition operators

JOURNAL OF APPROXIMATION THEORY

卷:164

Article

Li, Daniel^1,2  Queffelec, Herve³  Rodriguez-Piazza, Luis⁴ 

[1] Univ Lille Nord France, Lab Math Lens EA 2462, Fac Jean Perrin, U Artois, F-62300 Lens, France

[2] Federat CNRS Nord Pas de Calais FR 2956, Fac Sci Jean Perrin, F-62300 Lens, France

[3] Univ Lille Nord France, USTL, Lab Paul Painleve UMR CNRS 8524, F-59655 Villeneuve Dascq, France

[4] Univ Seville, Fac Matemat, Dept Anal Matemat & IMUS, E-41080 Seville, Spain

关键词: Approximation number;    Bergman space;    Carleson measure;    Composition operator;    Hardy space;    Interpolation sequence;    Reproducing kernel;    Weighted Bergman space;    Weighted shift;   

DOI  :  10.1016/j.jat.2011.12.003

来源: Elsevier

【 摘 要 】

We show that the approximation numbers of a compact composition operator on the Hardy space H-2 or on the weighted Bergman spaces B-alpha of the unit disk can tend to 0 arbitrarily slowly, but that they never tend quickly to 0: they cannot decay more rapidly than exponentially, and this speed of convergence is only obtained for symbols which do not approach the unit circle. We also give an upper bound and explicit an example. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free