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arXiv · 1311.6698

Abel averages and holomorphically pseudo-contractive maps in Banach spaces

Filippo Bracci·Yuri Kozitsky·David Shoikhet
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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.

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Filippo Bracci, Yuri Kozitsky, David Shoikhet. 2013-11-26. Abel averages and holomorphically pseudo-contractive maps in Banach spaces. https://arxiv.org/abs/1311.6698

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