空间s_p(a,L~q)中单位球面上的等距算子延拓问题
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摘要
讨论了空间s_p(a,L~q)中单位球面上的等距算子延拓问题,得到了空间s_p(a,L~q)中单位球面上的Lamperti等距能延拓到整个s_p(a,L~q)上.
In this paper, we present an isometric extension from the unit sphere of a subspace of s_p(a,L~q) to the whole space We obtain that the Lamperti isometric mapping of the unit sphere S(s_p(a,L~q)) into itself can be extended to an isometry on the whole space s_p(a,L~q).
In this paper, we present an isometric extension from the unit sphere of a subspace of s_p(a,L~q) to the whole space We obtain that the Lamperti isometric mapping of the unit sphere S(s_p(a,L~q)) into itself can be extended to an isometry on the whole space s_p(a,L~q).
引文
[1] TINGLEY D. Isometries of the unit spheres[J]. Geometriae Dedicata. 1987(22):371-378.
[2] DING GUANGGUI,LI JIE. Sharp corner points and isometric extension problem in Banach spaces[J]. J. Math. Anal.Appl. 2013(405):297-309.
[3] WANG RISHENG. Isometries on the lp-sum of C0(Ω,E) Type Spaces[J]. J. Math. Sci. Univ. Tokyo. 1996(3):471-493.
[4] FU XIAO HONG, STEVIC. The problem of isometric extension in the unit sphere of the space sp(α)[J].Nonlinear Anal. 2011(74):733-738.
[5] FU XIAO HONG. The isometric extension of the into mapping from the unit sphere S1(E) to S1(l∞(τ))[J].Acta Math. Sin(Engl. Ser.)2008,24(9):1475-1482.
[6] KADETS V, MARTIN M. Extension of isometries between unit spheres of finite-dimensional polyhedral Banach spaces[J]. J. Math. Anal. Appl. 2012(396):441-447.
[7] HOU ZHIBIN. The isometric extension of the into mapping between the unit spheres of AL~P-spaces(1＜p＜∞) [J]. Acta Math. Sin(Chin Ser.)2007, 50(6):1435-1440.
[2] DING GUANGGUI,LI JIE. Sharp corner points and isometric extension problem in Banach spaces[J]. J. Math. Anal.Appl. 2013(405):297-309.
[3] WANG RISHENG. Isometries on the lp-sum of C0(Ω,E) Type Spaces[J]. J. Math. Sci. Univ. Tokyo. 1996(3):471-493.
[4] FU XIAO HONG, STEVIC. The problem of isometric extension in the unit sphere of the space sp(α)[J].Nonlinear Anal. 2011(74):733-738.
[5] FU XIAO HONG. The isometric extension of the into mapping from the unit sphere S1(E) to S1(l∞(τ))[J].Acta Math. Sin(Engl. Ser.)2008,24(9):1475-1482.
[6] KADETS V, MARTIN M. Extension of isometries between unit spheres of finite-dimensional polyhedral Banach spaces[J]. J. Math. Anal. Appl. 2012(396):441-447.
[7] HOU ZHIBIN. The isometric extension of the into mapping between the unit spheres of AL~P-spaces(1＜p＜∞) [J]. Acta Math. Sin(Chin Ser.)2007, 50(6):1435-1440.