Extensions of endomorphisms of
Authors:
J. F. Feinstein and T. J. Oliver
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
Published electronically:
June 28, 2006
MathSciNet review:
2280180
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: For a compact space we consider extending endomorphisms of the algebra
to be endomorphisms of Arens-Hoffman and Cole extensions of
. Given a non-linear, monic polynomial
, with
semi-simple, we show that if an endomorphism of
extends to the Arens-Hoffman extension with respect to
, then it also extends to the simple Cole extension with respect to
. We show that the converse to this is false. For a locally connected, metric
we characterize the algebraically closed
in terms of the extendability of endomorphisms to Arens-Hoffman and to simple Cole extensions.
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Additional Information
J. F. Feinstein
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, England
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
DOI:
https://doi.org/10.1090/S0002-9939-06-08441-3
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
Article copyright:
© Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.