Cesàro function spaces fail the fixed point property

Astashkin, Sergei; Maligranda, Lech

doi:10.1090/S0002-9939-08-09599-3

Cesàro function spaces fail the fixed point property
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by Sergei V. Astashkin and Lech Maligranda

Proc. Amer. Math. Soc. 136 (2008), 4289-4294

DOI: https://doi.org/10.1090/S0002-9939-08-09599-3

Published electronically: June 26, 2008

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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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