Renormings of \(c_0\) and the minimal displacement problem

Łukasz Piasecki

Abstract


The aim of this paper is to show that for every Banach space \((X, \|\cdot\|)\) containing asymptotically isometric copy of the space \(c_0\) there is a bounded, closed and convex set \(C \subset X\) with the Chebyshev radius \(r(C) = 1\) such that for every \(k \geq 1 \) there exists a \(k\)-contractive mapping \(T : C \to C\) with \(\| x - Tx \| > 1 − 1/k\) for any \(x \in C\).

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DOI: http://dx.doi.org/10.17951/a.2014.68.2.85
Date of publication: 2015-05-23 16:29:45
Date of submission: 2015-05-09 13:53:37


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