Operator algebras from the discrete Heisenberg semigroup

Abstract

We study reflexivity and structure properties of operator algebras generated by representations of the discrete Heisenberg semi-group. We show that the left regular representation of this semi-group gives rise to a semi-simple reflexive algebra. We exhibit an example of a representation which gives rise to a non-reflexive algebra. En route, we establish reflexivity results for subspaces of $H^{\infty}(\bb{T})\otimes\cl B(\cl H)$.

References in corpus (2)

• Reflexivity of the translation-dilation algebras on L^2(R)
• Semicrossed Products and Reflexivity

Cited by in corpus (2)

• Ordinary differential equations in algebras of generalized functions
• Free multivariate w*-semicrossed products: reflexivity and the bicommutant property