• Bulletin of the Korean Mathematical Society
• /
• v.56 no.6
• /
• pp.1377-1384
• /
• 2019

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.

• Bulletin of the Korean Mathematical Society
• /
• v.29 no.2
• /
• pp.227-232
• /
• 1992

In this paper we prove that if (.ohm., .SIGMA., .mu.) is a non-purely atomic measure space and X is strictly convex, then X has the asymptotic-norming property II if and only if $L_{p}$ (X, .mu.), 1 < p < .inf., has the asymptotic-norming property II. And we prove that if $X^{*}$ is an Asplund space and strictly convex, then for any p, 1 < p < .inf., $X^{*}$ has the .omega.$^{*}$-ANP-II if and only if $L_{p}$ ( $X^{*}$, .mu.) has the .omega.$^{*}$-ANP-II.*/-ANP-II.