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Valuations on Banach Lattices

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

Authors: Tradacete, Pedro; Villanueva, Ignacio;

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

arXiv: http://arxiv.org/abs/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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	citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	12
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Top 10%
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Top 10%