Extended eigenvalues of composition operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:504

Article

Lacruz, Miguel^1,2  Leon-Saavedra, Fernando^3,4  Petrovic, Srdjan⁵  Rodriguez-Piazza, Luis^1,2 

[1] Univ Seville, Fac Matemat, Dept Anal Matemat, Ave Reina Mercedes, Seville 41012, Spain

[2] Univ Seville, Fac Matemat, Inst Matemat, Ave Reina Mercedes, Seville 41012, Spain

[3] Southern Fed Univ, Reg Math Ctr, Ave Univ, Cadiz 11405, Spain

[4] Univ Cadiz, Dept Matemat, Ave Univ, Cadiz 11405, Spain

[5] Western Michigan Univ, Dept Math, Kalamazoo, MI 49008 USA

关键词: Extended eigenvalue;    Composition operator;    Hardy space;    Linear fractional transformation;   

DOI  :  10.1016/j.jmaa.2021.125427

来源: Elsevier

【 摘 要 】

A complex scalar lambda is said to be an extended eigenvalue of a bounded linear operator A on a complex Hilbert space if there is a nonzero operator X such that AX = lambda XA. The results in this paper provide a full solution to the problem of computing the extended eigenvalues for those composition operators C-phi induced on the Hardy space H-2(D) by linear fractional transformations phi of the unit disk. (c) 2021 Universidad de Sevilla. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

【 授权许可】

Free