Extensions of endomorphisms of $C(X)$
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- by J. F. Feinstein and T. J. Oliver PDF
- Proc. Amer. Math. Soc. 135 (2007), 109-117 Request permission
Abstract:
For 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 a 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.References
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Additional Information
- J. F. Feinstein
- Affiliation: School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, England
- MR Author ID: 288617
- Email: Joel.Feinstein@nottingham.ac.uk
- T. J. Oliver
- Affiliation: School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, England
- Email: Thomas.Oliver@maths.nottingham.ac.uk
- Received by editor(s): October 14, 2004
- Received by editor(s) in revised form: July 21, 2005
- Published electronically: June 28, 2006
- Additional Notes: The second author would like to thank the EPSRC for providing support for this research
- Communicated by: N. Tomczak-Jaegermann
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 109-117
- MSC (2000): Primary 46J10, 47B48
- DOI: https://doi.org/10.1090/S0002-9939-06-08441-3
- MathSciNet review: 2280180