Sums of asymptotically midpoint uniformly convex spaces

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

doi:10.36045/bbms/1506477692

Sums of asymptotically midpoint uniformly convex spaces

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

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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 (Formula Presented) is asymptotically midpoint uniformly convex (AMUC) if and only if the spaces X_n are uniformly AMUC and E is uniformly monotone. We also show that L_p (X) is AMUC if and only if X is uniformly convex.

Original language	English
Pages (from-to)	439-446
Number of pages	8
Journal	Bulletin of the Belgian Mathematical Society - Simon Stevin
Volume	24
Issue number	3
DOIs	https://doi.org/10.36045/bbms/1506477692
State	Published - Sep 2017

Keywords

AMUC
asymptotic geometry
asymptotic moduli
Uniform convexity

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10.36045/bbms/1506477692

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KW - asymptotic geometry

KW - asymptotic moduli

KW - Uniform convexity

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Sums of asymptotically midpoint uniformly convex spaces

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