Browsing Mathematics by Author "Vujošević, Biljana"
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Vujošević, Biljana (Beograd , 2015)[more][less]
Abstract: In this doctoral dissertation we de ne the index of product systems of Hilbert B B modules over a unital C -algebra B. In detail, we prove that the set of all uniformly continuous units on a product system over a C -algebra B can be endowed with a structure of left-right Hilbert B B module after identifying similar units by the suitable equivalence relation and we use that construction to de ne the index of a given product system. We prove that such de ned index is a covariant functor from the category of continuous product systems to the category of two-sided BB modules. We prove that the index is subadditive with respect to the outer tensor product of product systems and we, also, prove additional properties of the index of product system that can be embedded into a spatial one (a product system that contains a central unital unit). We prove that such de ned index is a generalization of earlier de ned indices by Arveson (in the case B = C) and Skeide (in the case of spatial product systems). We, also, de ne the index of product systems in a di erent way and prove that the new de nition is equivalent to the previous one. Actually, it corresponds to Arveson's original de nition of the index. URI: http://hdl.handle.net/123456789/4235 Files in this item: 1
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