2025/05/22 by M.. Villamizar, Villamizar, Michael Alexánder Rincón, Timur Oikhberg +1
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2505.16775
openalex publication_date 2025/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a Banach lattice X, its lattice Schäffer constant is defined by: λ+(X)=inf\max\‖x+y‖,‖x-y‖\ \colon ‖x‖=‖y‖=1,x,y≥\bf0\. In this paper, we investigate this constant, as well as the companion parameter β(X)=inf\‖x\vee y‖ \colon \mbox‖x‖=‖y‖=1, x,y≥\bf0 and x\wedge y=\bf0\. Our main results fall into two groups. (1) We link the behavior of the parameters λ+ and β to the global properties of the lattice X. For instance, we prove that (i) if λ+(X)>1, then the Banach lattice X is a KB-space, and moreover, it satisfies a lower q-estimate for some q∈(1,∞); (ii) λ+(X)=1 if and only if X contains lattice-almost isometric copies of ℓ_∞2; and (iii) that λ+(X)=2 if and only if X is an abstract L-space. (2) We establish inequalities relating λ+(X) to the characteristics of monotonicity, ε0,m(X) and ε0,m(X). Along the way, we compute λ+(X) and β(X) for various Banach lattices X.