MATHEMATICAL ANALYSIS WITH APPLICATIONS Seminar

 

PROGRAM

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Plan rada Seminar iz matematičke analize sa primenama za MART 2024.

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Četvrtak, 28.03.2024. u 16:00, Kneza Mihaila 36, sala 301f i Online
Stefan Ivković, Mathematical Institute SASA
ON GNS-REPRESENTATIONS OF C*-VALUED POSITIVE SESQUILINEAR FORMS ON UNITAL QUASI *-ALGEBRAS
The concept of quasi *-algebras has originally been introduced by Lassner in the 80-is. The motivation for this concept comes from physics and several papers and monographs has been written in this field. Some of the concrete examples of quasi *-algebras are commutative and non-commutative L^p spaces. An important result in this field are GNS-representations of scalar valued positive sesquilinear forms on unital quasi *-algebras. In this talk, we shall present the results from the joint research with C. Trapani and G. Bellomonte. We shall first introduce the concept of quasi Banach spaces whose norm is induced by a C*-valued quasi inner product and we shall briefly discuss some aspects of the theory of closable operators and their adjoints on these spaces. Then we shall construct on these spaces GNS-representations of C*-valued positive sesquilinear forms on unital quasi *-algebras, as a generalization of the above mentioned results. Moreover, we shall illustrate the results on the concrete examples of non-commutative L^p spaces.
Finally, we shall present some applications of these results, such as a C*-valued GNS-representations of positive linear mappings from unital *-algebras into C*-algebras. Such mappings have an important role in quantum information theory and, by our GNS- representations, we obtain an explicit description of all such maps.

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