Publications de l'Institut Mathématique, Nouvelle Série Vol. 97(111), pp. 49–56 (2015) 

THE INDEX OF PRODUCT SYSTEMS OF HILBERT MODULES: TWO EQUIVALENT DEFINITIONSBiljana VujosevicFaculty of Mathematics, University of Belgrade, Belgrade, SerbiaAbstract: We prove that a conditionally completely positive definite kernel, as the generator of completely positive definite (CPD) semigroup associated with a continuous set of units for a product system over a $C^*$algebra $\mathcal{B}$, allows a construction of a Hilbert $\mathcal{B}\mathcal{B}$ module. That construction is used to define the index of the initial product system. It is proved that such definition is equivalent to the one previously given by Keckic and Vujosevic [\emph{On the index of product systems of Hilbert modules}, Filomat, to appear, ArXiv:1111.1935v1 [math.OA] 8 Nov 2011]. Also, it is pointed out that the new definition of the index corresponds to the one given earlier by Arveson (in the case $\mathcal{B}=\mathbb{C}$). Keywords: product system; Hilbert module; index Classification (MSC2000): 46L53;46L55 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 16 Apr 2015. This page was last modified: 21 Apr 2015.
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