Bishop-Phelps-Bollobas modulus of a uniformly non-square Banach space

Keywords: spiral conductive sphere, vertical dipole, compact operator

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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How to Cite
Soloviova, M. V. (1). Bishop-Phelps-Bollobas modulus of a uniformly non-square Banach space. Visnyk of V. N. Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics, 81, 4-9. https://doi.org/10.26565/2221-5646-2015-81-01
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