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Search: MSC category 47L55 ( Representations of (nonselfadjoint) operator algebras )

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1. CMB 2006 (vol 49 pp. 117)

Levene, R. H.
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 $SL_2(\R_+)$.

Categories:46K50, 47L55

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