Abstract
We introduce the notion of a positive spectral measure on a -algebra, taking values in the positive projections on a Banach lattice. Such a measure generates a bounded positive representation of the bounded measurable functions. If is a locally compact Hausdorff space and if is a positive representation of on a KB-space, then is the restriction to of such a representation generated by a unique regular positive spectral measure on the Borel -algebra of . The relation between a positive representation of on a Banach lattice and—if it exists—a generating positive spectral measure on the Borel -algebra are further investigated; here and elsewhere, phenomena occur that are specific for the ordered context.
Citation
Marcel de Jeu. Frejanne Ruoff. "Positive representations of , I." Ann. Funct. Anal. 7 (1) 180 - 205, February 2016. https://doi.org/10.1215/20088752-3462285
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