Acta Mathematica Sinica

, Volume 22, Issue 6, pp 1721–1724

The Isometric Extension of an Into Mapping from the Unit Sphere \( S{\left( {{\ell }^{\infty }_{{{\left( 2 \right)}}} } \right)} \) to \( S{\left( {L^{1} {\left( \mu \right)}} \right)} \)

ORIGINAL ARTICLES

DOI: 10.1007/s10114-005-0695-1

Cite this article as:
Ding, G.G. Acta Math Sinica (2006) 22: 1721. doi:10.1007/s10114-005-0695-1

Abstract

This is the first paper to consider the isometric extension problem of an into–mapping between the unit spheres of two different types of spaces. We prove that, under some conditions, an into–isometric mapping from the unit sphere \( S{\left( {{\ell }^{\infty }_{{{\left( 2 \right)}}} } \right)} \) to \( S{\left( {L^{1} {\left( \mu \right)}} \right)} \) can be (real) linearly isometrically extended.

Keywords

isometric mapping isometric extension 

MR (2000) Subject Classification

46A22 46B04 46B20 

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.School of Mathematical Science and LPMCNankai UniversityTianjin 300071P. R. China

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