Abstract:
A well known result in C*-algebra theory states that any two C*-norms on a *-algebra B turning it into a C*-algebra are necessarily equal. However, this conclusion breaks down when we abandon the hypothesis of completeness. In this talk, we will present criteria that guarantees uniqueness of the C*-norm on a *-algebra B, in the absence of completeness. We will show that a particularly interesting situation which fulfills our requirements appears when B is a Fréchet *-algebra whose topology can be defined by a differential seminorm, as originally introduced by Blackadar and Cuntz and later modified by Bhatt, Inoue and Ogi. In this context, we will prove uniqueness of the C*-norm for certain Fréchet *-algebras of pseudodifferential operators and to the noncommutative algebras of C-valued functions defined by Rieffel via a deformation quantization procedure, where C is a C*-algebra.
(Joint work with M. Forger and S.T. Melo).
Biography:
Rodrigo A. H. M. Cabral is a postdoc researcher at the Institute of Mathematics and Statistics of the University of São Paulo (IME-USP). He has a Bachelor's Degree in Pure Mathematics (2011) and Master's (2014) and Doctorate (2019) Degrees in Applied Mathematics, all obtained from University of São Paulo. His research focuses on infinite dimensional representation theory, locally convex *-algebras and their subsequent applications to mathematical physics.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.