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Rigid sets and nonexpansive mappings

Authors: Giovanni DiLena, Basilio Messano and Delfina Roux
Journal: Proc. Amer. Math. Soc. 125 (1997), 3575-3580
MSC (1991): Primary 47H09, 47H07, 47H10
MathSciNet review: 1415582
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Abstract: We introduce a new class of normed spaces (not necessarily finite dimensional), which contains the finite dimensional normed spaces with polyhedral norm. We study the properties of rigid sets of the spaces of this class and we apply the results to limit sets of the sequences of iterates of nonexpansive maps.

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Additional Information

Giovanni DiLena
Affiliation: Dipartimento di Matematica dell’Università, Via G. Fortunato, Campus Universitario - 70125 Bari, Italy

Basilio Messano
Affiliation: Dipartimento di Matematica e Applicazioni “R. Caccioppoli” dell’Università, Via Claudio 21 - 80125 Napoli, Italy

Delfina Roux
Affiliation: Dipartimento di Matematica “F. Enriques” dell’Università, Via Saldini 50 - 20133 Milano, Italy

Keywords: $S$-space, polyhedral norm, rigid sets, nonexpansive mappings, limit sets
Additional Notes: This work was performed under the auspices of M.U.R.S.T
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society

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