Extensions of endomorphisms of C(X)

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dc.creatorFeinstein, J. F.
dc.creatorOliver, T. J.
dc.date2004-10-01
dc.date.accessioned2026-07-07T05:12:47Z
dc.date.available2026-07-07T05:12:47Z
dc.descriptionFor a compact space X we consider extending endomorphisms of the algebra C(X) to be endomorphisms of Arens-Hoffman and Cole extensions of C(X). Given a non-linear, monic polynomial p in C(X)[t], with C(X)[t]/pC(X)[t] semi-simple, we show that if an endomorphism of C(X) extends to the Arens-Hoffman extension with respect to p then it also extends to the simple Cole extension with respect to p. We show that the converse to this is false. For locally connected, metric X we characterize the algebraically closed C(X), in terms of the extendability of endomorphisms to Arens-Hoffman and to simple Cole extensions.
dc.description12 pages latex, 2 figures
dc.identifierhttps://arxiv.org/abs/math/0410025
dc.identifierhttp://arxiv.org/abs/math/0410025
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72706
dc.subjectFunctional Analysis
dc.subject46J10;47B48
dc.titleExtensions of endomorphisms of C(X)
dc.typetext

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