A Ritt–Kreiss condition: Spectral localization and norm estimates
Volume 276 / 2024
Studia Mathematica 276 (2024), 171-193
MSC: Primary 47A10; Secondary 47A35, 47D03
DOI: 10.4064/sm231227-19-4
Published online: 25 June 2024
Abstract
A new condition is introduced by generalizing the Ritt and Kreiss operators, named the $(\alpha ,\beta )$-RK condition. Geometrical properties of the spectrum for $\beta \lt 1$ are studied and moreover it is shown that then if $\alpha + \beta = 1$ the operator is Ritt. Estimates for the power and power differences norms for this type of operators are also studied. Lastly, we apply this theory to obtain an interpolation result for Ritt and Kreiss operators on $L^p$ spaces.
