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

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

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.

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Veröffentlicht in:Taehan Suhakhoe hoebo 2019, Vol.56 (6), p.1377-1384
Hauptverfasser: Huang, Xujian, Jin, Xihong
Format: Artikel
Sprache:kor
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Zusammenfassung: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.
ISSN:1015-8634