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Isomorphically Expansive Mappings in $l_{2}$

Authors: J. García-Falset, A. Jiménez-Melado and E. Lloréns-Fuster
Journal: Proc. Amer. Math. Soc. 125 (1997), 2633-2636
MSC (1991): Primary 47H09, 47H10
MathSciNet review: 1389518
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Abstract: We show that for any renorming $\| \cdot \|$ of $\ell _{2}$, the well known fixed point free mappings by Kakutani, Baillon and others are not nonexpansive.

References [Enhancements On Off] (What's this?)

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  • [GKT] K. Goebel, W.A. Kirk and R.L. Thele. Uniformly Lipschitzian semigroups in Hilbert space. Canad. J. Math. 26 (1974), 1245-1256. MR 50:10919
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Additional Information

J. García-Falset
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universitat de València, 46100 Burjassot, Valencia, Spain

A. Jiménez-Melado
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain

E. Lloréns-Fuster

Keywords: Nonexpansive mappings, uniformly lipschitzian mappings, fixed points
Received by editor(s): November 28, 1995
Received by editor(s) in revised form: March 18, 1996
Additional Notes: This research has been partially supported by D.G.I.C.Y.T. PB93-1177-C02-02 and D.G.I.C.Y.T. PB94-1496.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society

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