Free quasi-Banach lattices

2025/12/04 by Salguero-Alarcón, Alberto, Tradacete, Pedro, Trejo-Arroyo, Nazaret
#06B25 #46B42. Secondary: 46M10 #47B60 #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 46A40

paper · doi:10.48550/arxiv.2512.05273

Abstract

We study different versions of free objects in the setting of quasi-Banach spaces and quasi-Banach lattices. Special attention is devoted to the free p-convex p-Banach lattice FpBL^(p)[E] generated by a p-natural quasi-Banach space E, for which we provide a functional representation by means of operators into L_p[0,1]. This representation yields, among other consequences: (1) Operators from a Banach space E to any p-convex (0

Citations

• Banach lattices with upper p-estimates: free and injective objects
• Geometry of unit balls of free Banach lattices, and its applications
• Free Banach lattices
• Free complex Banach lattices
• Lattice embeddings in free Banach lattices over lattices
• Free Banach lattices under convexity conditions
• A Godefroy-Kalton principle for free Banach lattices
• Amalgamation and injectivity in Banach lattices
• (p,q)-regular operators between Banach lattices
• The free Banach lattice generated by a Banach space
• Stability results on interpolation scales of quasi-Banach spaces and applications

Related

• Free Banach lattices
• Free dual spaces and free Banach lattices
• Free Banach lattices under convexity conditions
• Free objects in Banach space theory
• Free Banach lattices over pre-ordered Banach spaces