Abstract
This is a study of reflexivity and structure properties of operator algebras generated by representations of the Heisenberg semigroup.We briefly revise earlier joint work with S.C. Power [14] on the continuous Heisenberg semigroup. We then show that the (restricted) left regular representation of the discrete Heisenberg semigroup gives rise to a reflexive operator algebra, which is semisimple. An example of a representation giving rise to a nonreflexive algebra is presented.
Report on joint work with M. Anoussis (Aegean) and I.G. Todorov (Belfast) [2].
Mathematics Subject Classification (2010). Primary 47L75; Secondary 43A65, 47L99.
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Katavolos, A. (2014). Some Operator Algebras from Semigroups. In: Todorov, I., Turowska, L. (eds) Algebraic Methods in Functional Analysis. Operator Theory: Advances and Applications, vol 233. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0502-5_5
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DOI: https://doi.org/10.1007/978-3-0348-0502-5_5
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Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0501-8
Online ISBN: 978-3-0348-0502-5
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