The numerical ranges of automorphic composition operators

Authors
Bourdon, PS Shapiro, JH
Citation
Ps. Bourdon et Jh. Shapiro, The numerical ranges of automorphic composition operators, J MATH ANAL, 251(2), 2000, pp. 839-854
Citations number
23
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN journal
0022247X → ACNP
Volume
251
Issue
2
Year of publication
2000
Pages
839 - 854
Database
ISI
SICI code
0022-247X(20001115)251:2<839:TNROAC>2.0.ZU;2-2
Abstract
We investigate the shape of the numerical range for composition operators i nduced on the Hardy space H-2 by conformal automorphisms of the unit disc. We show that usually, but not always, such operators have numerical ranges whose closures are discs centered at the origin. Surprising open questions arise from our investigation. (C) 2000 Academic Press.