Bishop-Phelps-Bollobas modulus of a uniformly non-square Banach space
Abstract
Chica, Kadets, Martin and Soloviova demonstrated recently that the Bishop-Phelps-Bollobas modulus $\Phi^S_X$ of a Banach spaces $X$ can be estimated from above through the parameter of uniform non-squareness $\alpha(X)$: $\Phi^S_X(\varepsilon) \leq \sqrt{2\varepsilon}\,\sqrt{1- \frac{1}{3}\alpha(X)}$. In this short note we demonstrate that the right-hand side in the above theorem cannot be substituted by anything smaller than $\sqrt{2\varepsilon}\,\sqrt{1-\alpha(X)}$.
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References
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