Abel averages and holomorphically pseudo-contractive maps in Banach spaces
Complex Variables
2013-11-27 v1 Functional Analysis
Abstract
A class of maps in a complex Banach space is studied, which includes both unbounded linear operators and nonlinear holomorphic maps. The defining property, which we call {\sl pseudo-contractivity}, is introduced by means of the Abel averages of such maps. We show that the studied maps are dissipative in the spirit of the classical Lumer-Phillips theorem. For pseudo-contractive holomorphic maps, we establish the power convergence of the Abel averages to holomorphic retractions.
Keywords
Cite
@article{arxiv.1311.6698,
title = {Abel averages and holomorphically pseudo-contractive maps in Banach spaces},
author = {Filippo Bracci and Yuri Kozitsky and David Shoikhet},
journal= {arXiv preprint arXiv:1311.6698},
year = {2013}
}