The problem of continuity for representable functionals on Banach quasi *-algebras

Abstract: A way to study problems concerning quantum statistical mechanics is to consider locally convex quasi *-algebras, for which Banach quasi *-algebras constitute a special class. For example, Banach quasi *-algebras can be obtained by taking the completion of a *-algebra $A_0$ with respect to a norm $|| \cdot ||$ for which the multiplication is (only) separately continuous. In the (locally convex) quasi *-algebras setting, a relevant role is played by representable functionals. Roughly speaking, a linear functional will be called representable if it allows a GNS-like construction.

In this talk, we discuss the problem of continuity for these functionals and some related results. We begin our discussion by looking at the properties of representable (and continuous) functionals, especially in the simplest case of Hilbert quasi *-algebras. This discussion leads naturally to look at the problem of continuity for these functionals. Hence, we examine the approaches to study this problem. If time permits, we will discuss some applications. The first part of the talk is joint work with C. Trapani. The second part is joint work with M. Fragoulopoulou.

functional analysisgroup theoryoperator algebrasquantum algebra

Audience: researchers in the topic

Groups, Operators, and Banach Algebras Webinar

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