Sums of asymptotically midpoint uniformly convex spaces

S. J. Dilworth, Denka Kutzarova, N. Lovasoa Randrianarivony, Matthew Romney

Research output: Contribution to journalArticlepeer-review


We study the property of asymptotic midpoint uniform convexity for
infinite direct sums of Banach spaces, where the norm of the sum is
defined by a Banach space E with a 1-unconditional basis. We show that
a sum (∑∞n=1 Xn)E is asymptotically midpoint uniformly convex (AMUC) if
and only if the spaces Xn are uniformly AMUC and E is uniformly monotone.
We also show that Lp(X) is AMUC if and only if X is uniformly convex.
Original languageEnglish (US)
Pages (from-to)439-446
Number of pages8
JournalBulletin of the Belgian Mathematical Society - Simon Stevin
Issue number3
StatePublished - 2017


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