The C*-algebra of SL(2,R)

TL;DR

This paper characterizes the $C^*$-algebra of $SL(2,R)$ using operator valued Fourier transform, demonstrating the norm controlled dual limit property through explicit computations.

Contribution

It provides a detailed analysis of the $C^*$-algebra of $SL(2,R)$ and establishes the norm controlled dual limit property via explicit Fourier transform calculations.

Findings

Fourier transform of the $C^*$-algebra satisfies the norm controlled dual limit property

Explicit computations characterize the $C^*$-algebra of $SL(2,R)$

Enhanced understanding of the harmonic analysis on $SL(2,R)$

Abstract

The $C^*$-algebra of the group $SL(2,{\mathbb R})$ is characterized using the operator valued Fourier transform. In particular, it is shown by explicit computations, that the Fourier transform of this $C^*$-algebra fulfills the norm controlled dual limit property.