J. Aust. Math. Soc.
75 (2003), 413422

On direct sums of Banach spaces and convexity




Takayuki Tamura
Graduate School of Social Sciences and Humanities
Chiba University
Chiba 2638522
Japan
tamura@le.chibau.ac.jp



Abstract

Let be Banach spaces and
a continuous convex function with some
appropriate conditions on a certain convex set in
. Let
be the direct sum of equipped with the norm associated with
. We characterize the strict, uniform, and
locally uniform convexity of
by means of the convex function
. As an application these convexities are
characterized for the
sum
(,
), which includes the wellknown facts for the
sum
in the case .

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