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Rigid sets and nonexpansive mappings
Author(s):
Giovanni
DiLena;
Basilio
Messano;
Delfina
Roux
Journal:
Proc. Amer. Math. Soc.
125
(1997),
3575-3580.
MSC (1991):
Primary 47H09, 47H07, 47H10
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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
Email:
roux@vmimat.mat.unimi.it
DOI:
10.1090/S0002-9939-97-04053-7
PII:
S 0002-9939(97)04053-7
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
Copyright of article:
Copyright
1997,
American Mathematical Society
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