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A characterization of \(B\)-convexity and \(J\)-convexity of Banach spaces. (English) Zbl 1136.46010

The authors characterize the \(B_n\)-convexity and \(J_n\)-convexity of a Banach space \(X\) using the \(\psi\)-direct sum \((X\oplus\cdots\oplus X)_\psi\), where \(\psi\) is a continuous convex function on a certain convex subset of \(\mathbb{R}^n\).

MSC:

46B20 Geometry and structure of normed linear spaces
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