Extension of phase-isometries between the unit spheres of atomic $L_p$-spaces for $p>0$
Bull. Korean Math. Soc. 2019 Vol. 56, No. 6, 1377-1384
https://doi.org/10.4134/BKMS.b180561
Published online November 30, 2019
Xujian Huang, Xihong Jin
Tianjin University of Technology; Tianjin University of Technology
Abstract : 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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