M. M. Roginskaya, V. S. Shul'man, “On Minkowski Sums of Many Small Sets”, Funktsional. Anal. i Prilozhen., 2018, Volume 52, Issue 3,Pages <nobr>88

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Brief communications

On Minkowski Sums of Many Small Sets

M. M. Roginskaya^ab, V. S. Shul'man^c

^a Chalmers University of Technology
^b University of Gothenburg, Department of Mathematical Sciences
^c Vologda State University

Abstract: It is proved that a weakly closed subset of a Banach space is convex if and only if it can be represented as the sum of sets of arbitrarily small diameter.

Keywords: Minkowski addition, infinite divisibility, weak compactness, convexity.

UDC: 517+514

Received: 22.06.2017

DOI: 10.4213/faa3502