Isometries between unit spheres of \(\ell^{\infty}\)-sum of strictly convex normed spaces

Authors

  • G.-G. Ding School of Mathematical Sciences, Nankai University
  • J.-Z. Li Chern Institute of Mathematics, Nankai University

Keywords:

Isometric extension, $\ell^\infty$-sum, Normed space, Strictly convex

Abstract

In this article, we prove that any surjective isometry between unit spheres of $\ell^{\infty}$-sum of strictly convex normed spaces can be extended to a linear isometry on the whole space, and solve isometric extension problem affirmatively in this case. 10.1017/S000497271300018X

Published

2013-09-27

Issue

Vol. 88 No. 3 (2013)

Section

Articles
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