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MAZUR–ULAM PROPERTY OF THE SUM OF TWO STRICTLY CONVEX BANACH SPACES

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

Published online by Cambridge University Press:  11 November 2015

JIAN-ZE LI
JIAN-ZE LI*
Affiliation:
Department of Mathematics, Tianjin University, Tianjin 300072, PR China email lijianze@tju.edu.cn
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Abstract

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In this article, we study the Mazur–Ulam property of the sum of two strictly convex Banach spaces. We give an equivalent form of the isometric extension problem and two equivalent conditions to decide whether all strictly convex Banach spaces admit the Mazur–Ulam property. We also find necessary and sufficient conditions under which the $\ell ^{1}$-sum and the $\ell ^{\infty }$-sum of two strictly convex Banach spaces admit the Mazur–Ulam property.

Keywords

Mazur–Ulam propertyisometric extension problemstrictly convex

MSC classification

Primary: 46B04: Isometric theory of Banach spaces
Secondary: 46B20: Geometry and structure of normed linear spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 3 , June 2016 , pp. 473 - 485
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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