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ISOMETRIES BETWEEN UNIT SPHERES OF THE ${\ell }^{\infty } $-SUM OF STRICTLY CONVEX NORMED SPACES

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  28 March 2013

GUANG-GUI DING  and
JIAN-ZE LI
GUANG-GUI DING
Affiliation:
School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China email ding_gg@nankai.edu.cn
JIAN-ZE LI*
Affiliation:
School of Science, Tianjin University, Tianjin 30072, China Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China
*
✉lijianze@yeah.net
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Abstract

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

Keywords

isometric extensionℓ∞-sumstrictly convex normed space

MSC classification

Secondary: 46B04: Isometric theory of Banach spaces 46B20: Geometry and structure of normed linear spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 3 , December 2013 , pp. 369 - 375
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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