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Operator algebras from the discrete Heisenberg semigroup

Part of: Abstract harmonic analysis Linear spaces and algebras of operators

Published online by Cambridge University Press:  08 November 2011

M. Anoussis ,
A. Katavolos  and
I. G. Todorov
M. Anoussis
Affiliation:
Department of Mathematics, University of the Aegean, Karlovassi, 83200 Samos, Greece
A. Katavolos
Affiliation:
Department of Mathematics, University of Athens, Panepistimioupolis, 15784 Athens, Greece
I. G. Todorov
Affiliation:
Department of Pure Mathematics, Queen's University Belfast, University Road, Belfast BT7 1NN, UK
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Abstract

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We study reflexivity and structural properties of operator algebras generated by representations of the discrete Heisenberg semigroup. We show that the left regular representation of this semigroup gives rise to a semi-simple reflexive algebra. We exhibit an example of a representation that gives rise to a non-reflexive algebra. En route, we establish reflexivity results for subspaces of .

Keywords

non-self-adjoint operator algebrareflexivityslice mapdiscrete Heisenberg semigroup

MSC classification

Secondary: 47L75: Other nonselfadjoint operator algebras 43A65: Representations of groups, semigroups, etc. 47L99: None of the above, but in this section
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 1 , February 2012 , pp. 1 - 22
Copyright
Copyright © Edinburgh Mathematical Society 2011

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