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On extension of isometries between unit spheres of $AL_p$-spaces $(0<p<\infty)$


Author: Wang Jian
Journal: Proc. Amer. Math. Soc. 132 (2004), 2899-2909
MSC (2000): Primary 46B04; Secondary 46A40
Published electronically: May 20, 2004
MathSciNet review: 2063109
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Abstract: In this paper, we study the extension of isometries between unit spheres of atomic $AL_p$-spaces $(0<p<\infty, p\neq2)$. We find a condition under which an isometry $T$ between unit spheres can be linearly isometrically extended. Moreover, we prove that every onto isometry between unit spheres of atomic $AL_p$-spaces $(0<p<\infty, p\neq2)$ can be linearly isometrically extended to the whole space.


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Additional Information

Wang Jian
Affiliation: Department of Mathematics, Nanjing University, Nanjing, 210093, People’s Republic of China; Department of Mathematics, Fujian Normal University, Fuzhou 350007, People’s Republic of China
Email: wjmath@nju.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-04-07482-9
Keywords: Atomic $AL_p$-space, isometric extension, atom
Received by editor(s): April 15, 2002
Received by editor(s) in revised form: June 24, 2002
Published electronically: May 20, 2004
Additional Notes: This work belongs to the Doctoral Programme Foundation of the Institution of Higher Education (20010055013) and the Programme of National Science Foundation of China (10271060). It was supported by the National Science Foundation of China (10171014) and the Foundation of Fujian Educational Committee (JA02166).
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2004 American Mathematical Society