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A counterexample to the Bishop-Phelps Theorem in complex spaces

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Abstract

The Bishop-Phelps Theorem asserts that the set of functionals which attain the maximum value on a closed bounded convex subsetS of a real Banach spaceX is norm dense inX *. We show that this statement cannot be extended to general complex Banach spaces by constructing a closed bounded convex set with no support points.

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Lomonosov, V. A counterexample to the Bishop-Phelps Theorem in complex spaces. Isr. J. Math. 115, 25–28 (2000). https://doi.org/10.1007/BF02810578

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  • DOI: https://doi.org/10.1007/BF02810578

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