On extension of isometries between unit spheres of $AL_p$-spaces $(0<p<\infty )$
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Abstract:
In this paper, we study the extension of isometries between unit spheres of atomic $AL_p$-spaces $(0<p<\infty ,\ p\neq 2)$. 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 $(0<p<\infty ,\ p\neq 2)$ can be linearly isometrically extended to the whole space.References
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Additional Information
- Wang Jian
- Affiliation: Department of Mathematics, Nanjing University, Nanjing, 210093, Peopleβs Republic of China; Department of Mathematics, Fujian Normal University, Fuzhou 350007, Peopleβs Republic of China
- Email: wjmath@nju.edu.cn
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 2899-2909
- MSC (2000): Primary 46B04; Secondary 46A40
- DOI: https://doi.org/10.1090/S0002-9939-04-07482-9
- MathSciNet review: 2063109