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 $SL_2(\R_+)$.