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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Cesàro function spaces fail the fixed point property


Authors: Sergei V. Astashkin and Lech Maligranda
Journal: Proc. Amer. Math. Soc. 136 (2008), 4289-4294
MSC (2000): Primary 46E30, 46B20, 46B42
Published electronically: June 26, 2008
MathSciNet review: 2431042
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Abstract: The Cesàro sequence spaces $ ces_{p}, 1 < p < \infty$, are reflexive but they have the fixed point property. In this paper we prove that in contrast to these sequence spaces the corresponding Cesàro function spaces $ Ces_{p}$ on both $ [0, 1]$ and $ [0, \infty)$ for $ 1 < p < \infty$ are not reflexive and they fail to have the fixed point property.


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Additional Information

Sergei V. Astashkin
Affiliation: Department of Mathematics and Mechanics, Samara State University, Acad. Pavlov 1, 443011 Samara, Russia
Email: astashkn@ssu.samara.ru

Lech Maligranda
Affiliation: Department of Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden
Email: lech@sm.luth.se

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09599-3
PII: S 0002-9939(08)09599-3
Keywords: Ces{\`a}ro sequence spaces, Ces{\`a}ro function spaces, fixed point property, asymptotically isometric copy of $ l^1$, $B$-convex spaces
Received by editor(s): October 18, 2007
Published electronically: June 26, 2008
Additional Notes: This research was supported by a grant from the Royal Swedish Academy of Sciences for cooperation between Sweden and the former Soviet Union (project 35440). The results were presented by the second author at The 8th International Conference on Fixed Point Theory and Its Applications, 16-22 July 2007, Chiang Mai, Thailand.
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.