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

Mitani, Ken-Ichi; Saito, Kichi-Suke

Banach J. Math. Anal. 1, No. 1, 33-42 (2007).

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 \(\mathbb{R}^n\).

Reviewer: Satit Saejung (Khon Kaen)

MSC:

46B20

Geometry and structure of normed linear spaces

Keywords:

\(B_n\)-convexity; \(J_n\)-convexity; \(\psi\)-direct sum