Solid extensions of the Cesaro operator On the Hardy space H2(D)

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:407

Article

Curbera, Guillermo P.¹  Ricker, Werner J.² 

[1] Univ Seville, Fac Matemat, E-41080 Seville, Spain

[2] Katholische Univ Eichstatt Ingolstadt, Math Geogr Fak, D-85072 Eichstatt, Germany

关键词: Cesaro operator;    Hardy space;    Solid core;    Multipliers;   

DOI  :  10.1016/j.jmaa.2013.05.027

来源: Elsevier

【 摘 要 】

We introduce and study the largest Banach space of analytic functions on the unit disc which is solid for the coefficient-wise order and to which the classical Cesar operator C: H-2 -> H-2 can be continuously extended, while still maintaining its values in H-2. Properties of this Banach space H(ces(2)) as well as a characterization of individual analytic functions which belong to H(ces(2)) are presented. In addition, both the multiplier space of H(ces(2)) and the spectrum of C : H(ces(2)) -> H(ces(2)) are determined. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free