2025/05/29 by Paolo Leonetti, Leonetti, Paolo, Cihan Orhan +1 · 1 citation
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #General Topology (math.GN)
paper · pdf · doi:10.48550/arxiv.2505.23263
openalex publication_date 2025/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given an ideal I on ω, we denote by SL(I) the family of positive normalized linear functionals on ℓ_∞ which assign value 0 to all characteristic sequences of sets in I. We show that every element of SL(I) is a Choquet average of certain ultrafilter limit functionals. Also, we prove that the diameter of SL(I) is 2 if and only if I is not maximal, and that the latter claim can be considerably strengthened if I is meager. Lastly, we provide several applications: for instance, recovering a result of Freedman in [Bull. Lond. Math. Soc. 13 (1981), 224--228], we show that the family of bounded sequences for which all functionals in SL(I) assign the same value coincides with the closed vector space of bounded I-convergent sequences.