On one-sided primitivity of Banach algebras

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dc.creatorCrabb, M. J.
dc.creatorDuncan, J.
dc.creatorMcGregor, C. M.
dc.date2008-07-31
dc.date2009-04-28
dc.date.accessioned2026-07-07T13:08:38Z
dc.date.available2026-07-07T13:08:38Z
dc.descriptionLet $S$ be the semigroup with identity, generated by $x$ and $y$, subject to $y$ being invertible and $yx=xy^2$. We study two Banach algebra completions of the semigroup algebra $\mathbb{C}S$. Both completions are shown to be left-primitive and have separating families of irreducible infinite-dimensional right modules. As an appendix, we offer an alternative proof that $\mathbb{C}S$ is left-primitive but not right-primitive. We show further that, in contrast to the completions, every irreducible right module for $\mathbb{C}S$ is finite dimensional and hence that $\mathbb{C}S$ has a separating family of such modules.
dc.description14 pages. To appear, with minor changes, in the Proceedings of the Edinburgh Mathematical Society
dc.identifierhttps://arxiv.org/abs/0807.5033
dc.identifierhttp://arxiv.org/abs/0807.5033
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/228480
dc.subjectFunctional Analysis
dc.subject46H20
dc.titleOn one-sided primitivity of Banach algebras
dc.typetext

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