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ON THE SETS OF GTEAUX NON-DIFFERENTIABILITY OF LIPSCHITZ ISOMORPHISM BETWEEN BANACH SPACES

ON THE SETS OF GTEAUX NON-DIFFERENTIABILITY OF LIPSCHITZ ISOMORPHISM BETWEEN BANACH SPACES
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摘要 We prove that for every Lipschitz isomorphism f from a separable Hilbert space H to a Banach space Y with Radon-Nikodym property, there is a bounded surjective linear operator T: H → Y so that (f + T)-1 (NG(f-1)) is a r-null set of H, where NG(f-1) is the set of all the points of Gateaux non-diiTerentiability of f -1. We prove that for every Lipschitz isomorphism f from a separable Hilbert space H to a Banach space Y with Radon-Nikodym property, there is a bounded surjective linear operator T: H → Y so that (f + T)-1 (NG(f-1)) is a r-null set of H, where NG(f-1) is the set of all the points of Gateaux non-diiTerentiability of f -1.
作者 Yingbin Ruan
机构地区 Dept.of Math.
出处 《Annals of Applied Mathematics》 2015年第3期324-328,共5页 应用数学年刊(英文版)
基金 supported by the National Natural Science Foundation of China(11171066) the Natural Science Foundation of Fujian Province(2013J01003)
关键词 Lipschitz isomorphism Gateaux differentiability F-null sets Lipschitz isomorphism Gateaux differentiability F-null sets
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