1. CMB 2006 (vol 49 pp. 117)
|A Double Triangle Operator Algebra From $SL_2(\R)$ |
We consider the w$^*$-closed operator algebra $\cA_+$ generated by the image of the semigroup $SL_2(\R_+)$ under a unitary representation $\rho$ of $SL_2(\R)$ on the Hilbert~space $L_2(\R)$. We show that $\cA_+$ is a reflexive operator algebra and $\cA_+=\Alg\cD$ where $\cD$ is a double triangle subspace lattice. Surprisingly, $\cA_+$ is also generated as a w$^*$-closed algebra by the image under $\rho$ of a strict subsemigroup of $SL_2(\R_+)$.