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Normal structure and fixed point property

Published online by Cambridge University Press:  18 May 2009

J. García-Falset  and
E. Lloréns-Fuster
J. García-Falset
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Doctor Moliner, 50, 46100 Burjasot, Valencia, Spain
E. Lloréns-Fuster
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Doctor Moliner, 50, 46100 Burjasot, Valencia, Spain
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The most classical sufficient condition for the fixed point property of non-expansive mappings FPP in Banach spaces is the normal structure (see [6] and [10]). (See definitions below). Although the normal structure is preserved under finite lp-product of Banach spaces, (1<p≤∞), (see Landes, [12], [13]), not too many positive results are known about the normal structure of an l1,-product of two Banach spaces with this property. In fact, this question was explicitly raised by T. Landes [12], and M. A. Khamsi [9] and T. Domíinguez Benavides [1] proved partial affirmative answers. Here we give wider conditions yielding normal structure for the product X1⊗1X2.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 38 , Issue 1 , January 1996 , pp. 29 - 37
Copyright
Copyright © Glasgow Mathematical Journal Trust 1996

References

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