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On a conjecture of L. Veselý. (English) Zbl 0894.46012
Summary: The aim of this note is to give a negative answer to a question raised by L. Veselý during the Winter School held in Benešova Hora in January 1996. We show that there exists a separable Banach space \(Z\) such that for any point \(z\) in the unit sphere there is some linear functional which strongly exposes the unit ball at \(z\), but on which there is a linear functional which exposes the unit ball without exposing it strongly.
46B20 Geometry and structure of normed linear spaces
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