Geometry of unit balls of free Banach lattices, and its applications

2023/03/09 by Timur Oikhberg, Oikhberg, Timur · 3 citations
Mathematics · #46B28 #46B42 #47B10 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2303.05209

openalex publication_date 2023/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We begin by describing the unit ball of the free p-convex Banach lattice over a Banach space E (denoted by FBL^(p)[E]) as a closed solid convex hull of an appropriate set. Based on it, we show that, if a Banach space E has the λ-Approximation Property, then FBL^(p)[E] has the λ-Positive Approximation Property. Further, we show that operators u ∈ B(E,F) (where E and F are Banach spaces) which extend to lattice homomorphisms from FBL^(q)[E] to FBL^(p)[F] are precisely those whose adjoints are (q,p)-mixing. Related results are also obtained for free lattices with an upper p-estimate.

Cited by

• Free quasi-Banach lattices
• Compact positive multilinear operators on Banach lattices
• Complemented subspaces of Banach lattices

Related

• Free Banach lattices
• Free Banach lattices under convexity conditions
• Free quasi-Banach lattices
• Free Banach lattices over pre-ordered Banach spaces
• Banach lattices with upper p-estimates: free and injective objects