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A nonlinear map for midpoint locally uniformly rotund renorming

Published online by Cambridge University Press:  17 April 2009

S. Lajara  and
A.J. Pallars
S. Lajara
Affiliation:
Departamento de Matemticas, Universidad de Castilla La Mancha, Escuela Politcnica Superior de Albacete, Edificio Infante Don Juan Manuel, Campus Universitario, 02071 Albacete, Spain, email: sebastian.lajara@uclm.es
A.J. Pallars
Affiliation:
Departamento de Matemticas, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain, e-mail: apall@um.es
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We provide a criterion for midpoint locally uniformly rotund renormability of normed spaces involving the class of σ-slicely continuous maps, recently introduced by Moltó, Orihuela, Troyanski and Valdiva in 2003. As a consequence of this result, we obtain a theorem of G. Alexandrov concerning the three space problem for midpoint locally uniformly rotund renormings of Banach spaces.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 72 , Issue 1 , August 2005 , pp. 39 - 44
Copyright
Copyright © Australian Mathematical Society 2005

References

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