【摘 要】
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Assume that X and Y are real Banach spaces with the same finite dimension.In this paper we show that if a standard coarse isometry f :X → Y satisfies an integral con-vergence condition or weak stability on a basis,then there exists a surjective linear iso
【机 构】
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School of Mathematical Science,Xiamen University,Xiamen 361005,China
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Assume that X and Y are real Banach spaces with the same finite dimension.In this paper we show that if a standard coarse isometry f :X → Y satisfies an integral con-vergence condition or weak stability on a basis,then there exists a surjective linear isometry U :X → Y such that ||f(x)-Ux|| =o(||x||) as ||x|| → ∞.This is a generalization about the result of Lindenstrauss and Szankowski on the same finite dimensional Banach spaces without the assumption of surjectivity.As a consequence,we also obtain a stability result for ε-isometries which was established by Dilworth.
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