Valuations on Banach Lattices

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 14 Jun 2018Embargo end date: 01 Jan 2017 Spain English Publisher:Oxford University Press (OUP)Journal:International Mathematics Research Notices, volume 2,020, pages 2,468-2,500 (issn: 1073-7928, eissn: 1687-0247,

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Authors: Tradacete, Pedro; Villanueva, Ignacio;

doi: 10.1093/imrn/rny129 , 10.48550/arxiv.1711.11558

arXiv: 1711.11558

handle: 10261/231213

Valuations on Banach Lattices

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Abstract

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 $L_p(\mu )$, 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.

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Spain

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Keywords

Mathematics - Functional Analysis, 52B45, 46B42, 52A30, 46E30, Mathematics - Metric Geometry, FOS: Mathematics, Metric Geometry (math.MG), Functional Analysis (math.FA)

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