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2007 A characterization of B-convexity and J-convexity of Banach spaces
Ken-Ichi Mitani, Kichi-Suke Saito
Banach J. Math. Anal. 1(1): 33-42 (2007). DOI: 10.15352/bjma/1240321553

Abstract

In [K.-I. Mitani and K.-S. Saito, J. Math. Anal. Appl. 327 (2007), 898-907] we characterized the strict convexity, uniform convexity and uniform non-squareness of Banach spaces using $\psi$-direct sums of two Banach spaces, where $\psi$ is a continuous convex function with some appropriate conditions on $[0,1]$. In this paper, we characterize the $B_n$-convexity and $J_n$-convexity of Banach spaces using $\psi$-direct sums of $n$ Banach spaces, where $\psi$ is a continuous convex function with some appropriate conditions on a certain convex subset of $\mathbb R^n$.

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Ken-Ichi Mitani. Kichi-Suke Saito. "A characterization of B-convexity and J-convexity of Banach spaces." Banach J. Math. Anal. 1 (1) 33 - 42, 2007. https://doi.org/10.15352/bjma/1240321553

Information

Published: 2007
First available in Project Euclid: 21 April 2009

zbMATH: 1136.46010
MathSciNet: MR2350192
Digital Object Identifier: 10.15352/bjma/1240321553

Subjects:
Primary: 46B20
Secondary: 46B25

Keywords: $\psi$-direct sum , ‎absolute norm , B-convexity , J-convexity , superreflexivity

Rights: Copyright © 2007 Tusi Mathematical Research Group

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