• 대한수학회보
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• 제56권6호
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• pp.1377-1384
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• 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.

• 대한수학회보
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• 제29권2호
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• pp.227-232
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• 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.