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Bull. Korean Math. Soc. 2019; 56(6): 1377-1384

Online first article October 24, 2019      Printed November 30, 2019

https://doi.org/10.4134/BKMS.b180561

Copyright © The Korean Mathematical Society.

Extension of phase-isometries between the unit spheres of atomic $L_p$-spaces for $p>0$

Xujian Huang, Xihong Jin

Tianjin University of Technology; Tianjin University of Technology

Abstract

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In this paper, we prove that for every surjective phase-iso\-metry between the unit spheres of real atomic $L_p$-spaces for $p>0$, its positive homogeneous extension is a phase-isometry which is phase equivalent to a linear isometry.

Keywords: extension of phase-isometries, unit sphere, atomic $L_p$-spaces

MSC numbers: 46B04, 46B20

Supported by: The authors are supported by the Natural Science Foundation of China, Grant No. 11371201, 11201337, 11201338.

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