Continuity properties of sequentially asymptotically center-complete spaces. (English) Zbl 1350.41032
Summary: We obtain formulae to calculate the asymptotic center and radius of bounded sequences in \(\mathcal C_0(L)\) spaces. We also study the existence of continuous selectors for the asymptotic center map in general Banach spaces. In Hilbert spaces, even a Hölder-type estimation is given.
MSC:
| 41A50 | Best approximation, Chebyshev systems |
| 46E15 | Banach spaces of continuous, differentiable or analytic functions |
References:
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