Banach $\widetilde{\mathbb C}$-algebras

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dc.creatorVernaeve, Hans
dc.date2008-11-11
dc.date.accessioned2026-07-07T10:17:30Z
dc.date.available2026-07-07T10:17:30Z
dc.descriptionWe study Banach $\widetilde{\mathbb C}$-algebras, i.e., complete ultra-pseudo-normed algebras over the ring $\widetilde{\mathbb C}$ of Colombeau generalized complex numbers. We develop a spectral theory in such algebras. We show by explicit examples that important parts of classical Banach algebra theory do not hold for general Banach $\widetilde{\mathbb C}$-algebras and indicate a particular class of Banach $\widetilde{\mathbb C}$-algebras that overcomes these limitations to a large extent. We also investigate C*-algebras over $\widetilde{\mathbb C}$.
dc.description36 pages
dc.identifierhttps://arxiv.org/abs/0811.1742
dc.identifierhttp://arxiv.org/abs/0811.1742
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173874
dc.subjectFunctional Analysis
dc.subject46F30 (Primary) 46S10 (Secondary)
dc.titleBanach $\widetilde{\mathbb C}$-algebras
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