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NONEXPANSIVE MAPPINGS ON THE UNIT SPHERES OF SOME BANACH SPACES

Part of: Normed linear spaces and Banach spaces; Banach lattices Topological linear spaces and related structures

Published online by Cambridge University Press:  19 June 2009

DONG-NI TAN
DONG-NI TAN*
Affiliation:
School of Mathematical Sciences, Nankai University, Tianjin 300071, PR China (email: [email protected])
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Abstract

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We characterize surjective nonexpansive mappings between unit spheres of ℒ∞(Γ)-type spaces. We show that such mappings turn out to be isometries and can be extended to linear isometries on the whole space ℒ∞(Γ).

Keywords

nonexpansive mappingisometric extensionℒ∞(Γ)-type spaces

MSC classification

Secondary: 46A22: Theorems of Hahn-Banach type; extension and lifting of functionals and operators 46B20: Geometry and structure of normed linear spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 1 , August 2009 , pp. 139 - 146
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

This work was partially supported by Research Foundation for Doctor Programme (20070055010) and National Natural Science Foundation of China (10571090).

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