A Double Triangle Operator Algebra From SL2(ℝ+)

Abstract

AbstractWe consider the w*-closed operator algebra generated by the image of the semigroup SL2(ℝ+) under a unitary representation ρ of SL2(ℝ) on the Hilbert space L2(ℝ). We show that is a reflexive operator algebra and = Alg where is a double triangle subspace lattice. Surprisingly, is also generated as a w*-closed algebra by the image under ρ of a strict subsemigroup of SL2(ℝ+).