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arXiv · 1301.3396

Stability of Banach spaces via nonlinear $\varepsilon$-isometries

Duanxu Dai·Yunbai Dong
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Abstract

In this paper, we prove that the existence of an $\varepsilon$-isometry from a separable Banach space $X$ into $Y$ (the James space or a reflexive space) implies the existence of a linear isometry from $X$ into $Y$. Then we present a set valued mapping version lemma on non-surjective $\varepsilon$-isometries of Banach spaces. Using the above results, we also discuss the rotundity and smoothness of Banach spaces under the perturbation by $\varepsilon$-isometries.

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Duanxu Dai, Yunbai Dong. 2013-01-15. Stability of Banach spaces via nonlinear $\varepsilon$-isometries. https://doi.org/10.1016/j.jmaa.2014.01.028

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