Valuations on Banach lattices

2017/11/30 by Tradacete, Pedro, Villanueva, Ignacio
#46B42 #46E30 #52A30 #52B45 #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1711.11558

Abstract

We provide a general framework for the study of valuations on Banach lattices. This complements and expands several recent works about valuations on function spaces, including L_p(μ), Orlicz spaces and spaces C(K) of continuous functions on a compact Hausdorff space. In particular, we study decomposition properties, boundedness and integral representation of continuous valuations.

Related

• Algebraic structures on valuations, their properties and applications
• SL(n) covariant vector-valued valuations on Orlicz spaces
• Banach-lattice isomorphisms of C₀(K,X) spaces which determine the locally compact spaces K
• Lattice Valuations: a Generalisation of Measure and Integral
• Continuous valuations on the space of Lipschitz functions on the sphere