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Nonsurjective Coarse Isometries of Uniformly Convex Banach Spaces

open access: yesJournal of Function Spaces
We apply Pisier’s inequality to establish the stability property of nonsurjective coarse isometries from a Banach space to a uniformly convex space. Making use of this result, we extend some known conclusions on (ε, p) isometries of Hilbert spaces and Lq spaces.
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Uniformly non-$l^{(1)}$ and B-convex Banach spaces [PDF]

open access: yesStudia Mathematica, 1973
Giesy, D. P., James, R. C.
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Strongly unique best approximation in uniformly convex Banach spaces

open access: yesJournal of Approximation Theory, 1989
Let Y be a closed subspace of a Banach space X. An element \(z\in Y\) is called a strongly unique best approximation of order \(\alpha\) \((\alpha >1)\) at x, if for some \(M>0\) there exists \(\gamma =\gamma (x,M)>0\) such that, for all \(y\in Y\) with \(\| y-z\| \leq M\), \(\| y-x\| \geq \| z-x\| +\gamma \| y-z\|^{\alpha}.\) Results concerning strong
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