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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 $H^{infty}(bb{T})otimescl B(cl H)$.
The residual finite-dimensionality of a $mathrm{C}^*$-algebra is known to be encoded in a topological property of its space of representations, stating that finite-dimensional representations should be dense therein. We extend this paradigm to genera
We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar multipliers of a
We study subproduct systems in the sense of Shalit and Solel arising from stochastic matrices on countable state spaces, and their associated operator algebras. We focus on the non-self-adjoint tensor algebra, and Viselters generalization of the Cunt
We study comparison properties in the category Cu aiming to lift results to the C*-algebraic setting. We introduce a new comparison property and relate it to both the CFP and $omega$-comparison. We show differences of all properties by providing exam
We study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. We develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint theory to