A resolvent condition implying power boundedness

Authors
Nagy, B Zemanek, J
Citation
B. Nagy et J. Zemanek, A resolvent condition implying power boundedness, STUD MATH, 134(2), 1999, pp. 143-151
Citations number
33
Categorie Soggetti
Mathematics
Journal title
STUDIA MATHEMATICA
ISSN journal
00393223 → ACNP
Volume
134
Issue
2
Year of publication
1999
Pages
143 - 151
Database
ISI
SICI code
0039-3223(1999)134:2<143:ARCIPB>2.0.ZU;2-U
Abstract
The Ritt and Kreiss resolvent conditions are related to the behaviour of th e powers and their various means. In particular, it is shown that the Ritt condition implies the power boundedness. This improves the Nevanlinna chara cterization of the sublinear decay of the differences of the consecutive po wers in the Esterle-Katznelson-Tzafriri theorem, and actually characterizes the analytic Ritt condition by two geometric properties of the powers.