More on stability of almost surjective ε-isometries of Banach spaces

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• 作者：LiXin Cheng ; QinRui Shen ; Wen Zhang ; Yu Zhou
• 关键词：ε ; isometry ; stability ; sharp estimate ; Banach space
• 刊名：Science China Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：60
• 期：2
• 页码：277-284
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Applications of Mathematics;
• 出版者：Science China Press
• ISSN：1869-1862
• 卷排序：60

文摘

Let X and Y be two Banach spaces, and f: X → Y be a standard ε-isometry for some ε ≥ 0. In this paper, by using a recent theorem established by Cheng et al. (2013–2015), we show a sufficient condition guaranteeing the following sharp stability inequality of f: There is a surjective linear operator T: Y → X of norm one so that $$\left\| {Tf(x) - x} \right\| \leqslant 2\varepsilon , for all x \in X.$$As its application, we prove the following statements are equivalent for a standard ε-isometry f: X → Y:(i)lim inf_t→∞ dist(ty, f(X))/|t| < 1/2, for all y ∈ S_Y;