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Cesàro function spaces fail the fixed point property |
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| Authors: | Sergei V. Astashkin Lech Maligranda |
| Affiliation: | Department of Mathematics and Mechanics, Samara State University, Acad. Pavlov 1, 443011 Samara, Russia ; Department of Mathematics, Lulea University of Technology, SE-971 87 Lulea, Sweden |
| Abstract: | The Cesàro sequence spaces  , 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  on both ![$ [0, 1]$](http://www.ams.org/proc/2008-136-12/S0002-9939-08-09599-3/gif-abstract0/img3.gif){kind=small} and  for  are not reflexive and they fail to have the fixed point property. |
| Keywords: | Ces{`a}ro sequence spaces Ces{`a}ro function spaces fixed point property asymptotically isometric copy of $ l^1$ $B$-convex spaces |
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