arXiv subjects

Sepideh Rezvani

Publications and source records attributed to Sepideh Rezvani.

2 recordsLinked to original sources

arXiv2017

Harmonic analysis approach to Gromov--Hausdorff convergence for noncommutative tori

We show that the rotation algebras are limit of matrix algebras in a very strong sense of convergence for algebras with additional Lipschitz structure. Our results generalize to higher dimensional noncommutative tori and operator valued coefficients. In contrast to previous results by Rieffel, Li, Kerr, and Latrémolière we use Lipschitz norms induced by the `carré du champ' of certain natural dynamical systems, including the heat semigroup.

math.OA↗

arXiv2014

Operator-Valued Kirchberg Theory

In this paper, we will follow Kirchberg's categorical perspective to establish new notions of WEP and QWEP relative to a C$^*$-algebra, and develop similar properties as in the classical WEP and QWEP. Also we will show some examples of relative WEP and QWEP to illustrate the relations with the classical cases. Finally we will apply our notions to recent results on C$^*$-norms.

math.OA↗