Two Generalizations of Property (II) and their characterization

2025/03/10 by Basu, Sudeshna, Seal, Susmita
#46B20 #46B28 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2503.06905

Abstract

The concept of Property (II) was introduced and characterized by Chen and Lin \citeCL. In this work, given a compatiable collection of bounded sets A, we provide a complete characterization of two generalizations of Property (II) : (i) every closed convex set A∈ A is an intersection of closed convex hulls of finitely many balls and (ii) for every closed convex set A∈ A and β\geqslant 0, A+βB_X is an intersection of closed convex hulls of finitely many balls.

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