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http://dx.doi.org/10.4134/BKMS.b180561

EXTENSION OF PHASE-ISOMETRIES BETWEEN THE UNIT SPHERES OF ATOMIC Lp-SPACES FOR p > 0  

Huang, Xujian (Department of Mathematics Tianjin University of Technology)
Jin, Xihong (Department of Mathematics Tianjin University of Technology)
Publication Information
Bulletin of the Korean Mathematical Society / v.56, no.6, 2019 , pp. 1377-1384 More about this Journal
Abstract
In this paper, we prove that for every surjective phase-isometry 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;
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