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.