Geometric Characterization of Preduals of Injective Banach Lattices

2019/10/18 by A. G. Kusraev, S. S. Kutateladze, Kusraev, A. G. +1
Mathematics · #46B42 #46S99 #Advanced Banach Space Theory #Advanced Topology and Set Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.1910.08299

openalex publication_date 2019/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper deals with the study of Banach spaces whose duals are injective Banach lattices. Davies in 1967 proved that an ordered Banach space is an L¹-predual space if and only if it is a simplex space. In 2007 Duan and Lin proved that a real Banach space is an L¹-predual space if and only if its every four-point subset is centerable. We prove the counterparts of these remarkable results for injectives by the new machinery of Boolean valued transfer from L¹-spaces to injective Banach lattices.

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