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 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. (C) 2014 Elsevier Inc. All rights reserved.

Bracci, F., Kozitsky, Y., Shoikhet, D. (2015). Abel averages and holomorphically pseudo-contractive maps in Banach spaces. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 423(2), 1580-1593 [10.1016/j.jmaa.2014.10.079].

Abel averages and holomorphically pseudo-contractive maps in Banach spaces

Bracci F.;
2015-01-01

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 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. (C) 2014 Elsevier Inc. All rights reserved.
2015
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - GEOMETRIA
English
Holomorphic maps in Banach spaces; Unbounded operators; Abel averages; Fixed points
Bracci, F., Kozitsky, Y., Shoikhet, D. (2015). Abel averages and holomorphically pseudo-contractive maps in Banach spaces. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 423(2), 1580-1593 [10.1016/j.jmaa.2014.10.079].
Bracci, F; Kozitsky, Y; Shoikhet, D
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/233009
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