Nonexpansive mappings and expansive mappings on the unit spheres of some F-spaces

Authors

  • Dongni Tan

Keywords:

nonexpansive mapping, expansive mapping, Tingley's problem, $\ell^\beta(\Gamma)$ spaces

Abstract

This paper gives a characterization of nonexpansive mappings from the unit sphere of $\ell^{\beta}(\Gamma)$ onto the unit sphere of $\ell^{\beta}(\Delta)$ where $0<\beta\leq1$. By this result, we prove that such mappings are in fact isometries and give an affirmative answer to Tingley's problem in $\ell^{\beta}(\Gamma)$ spaces. We also show the same result holds for expansive mappings between unit spheres of $\ell^{\beta}(\Gamma)$ spaces without the surjectivity assumption. doi:10.1017/S0004972710000109

Published

2010-09-22

Issue

Vol. 82 (2010)

Section

Articles
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