Abstract
In this paper, we show that if V 0 is a 1-Lipschitz mapping between unit spheres of two AL p-spaces with p > 2 and −V 0(S 1(L p)) ⊂ V 0(S 1(L p)), then V 0 can be extended to a linear isometry defined on the whole space. If 1 < p < 2 and V 0 is an “anti-1-Lipschitz” mapping, then V 0 can also be linearly and isometrically extended.
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Supported by National Natural Science Foundation of China (Grant No. 10871101) and Research Fund for the Doctoral Program of Higher Education (Grant No. 20060055010)
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Ding, G.G. On linearly isometric extensions for 1-Lipschitz mappings between unit spheres of AL p-spaces (p > 2). Acta. Math. Sin.-English Ser. 26, 331–336 (2010). https://doi.org/10.1007/s10114-010-8266-5
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DOI: https://doi.org/10.1007/s10114-010-8266-5