Isomorphically expansive mappings in $l_2$
HTML articles powered by AMS MathViewer
- by J. García-Falset, A. Jiménez-Melado and E. Lloréns-Fuster PDF
- Proc. Amer. Math. Soc. 125 (1997), 2633-2636 Request permission
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
- Baillon, J.B. Quelques aspects de la théorie des points fixed dans les espaces de Banach, I, Séminaire d’Analyse Fonctionelle de l’Ecole Polytecnique, no. VII, 1978-79.
- Kazimierz Goebel and W. A. Kirk, Topics in metric fixed point theory, Cambridge Studies in Advanced Mathematics, vol. 28, Cambridge University Press, Cambridge, 1990. MR 1074005, DOI 10.1017/CBO9780511526152
- K. Goebel, W. A. Kirk, and R. L. Thele, Uniformly Lipschitzian families of transformations in Banach spaces, Canadian J. Math. 26 (1974), 1245–1256. MR 358453, DOI 10.4153/CJM-1974-119-9
- M. A. Khamsi, Normal structure for Banach spaces with Schauder decomposition, Canad. Math. Bull. 32 (1989), no. 3, 344–351. MR 1010075, DOI 10.4153/CMB-1989-050-7
- Daryl Tingley, Noncontractive uniformly Lipshitzian semigroups in Hilbert space, Proc. Amer. Math. Soc. 92 (1984), no. 3, 355–361. MR 759652, DOI 10.1090/S0002-9939-1984-0759652-X
Additional Information
- J. García-Falset
- Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universitat de València, 46100 Burjassot, Valencia, Spain
- Email: jesus.garcia@uv.es
- A. Jiménez-Melado
- Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain
- Email: melado@ccuma.sci.uma.es
- E. Lloréns-Fuster
- Email: enrique.llorens@uv.es
- 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
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 2633-2636
- MSC (1991): Primary 47H09, 47H10
- DOI: https://doi.org/10.1090/S0002-9939-97-03845-8
- MathSciNet review: 1389518