The Index of Product Systems of Hilbert Modules: Two Equivalent Definitions
نویسندگان
چکیده
Abstract. 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 B, allows a construction of a Hilbert B−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 Kečkić and Vujošević [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 B = C).
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