Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran
Copyright © 2010 Davood Alimohammadi and Sirous Moradi . This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a compact Hausdorff topological space and let and
denote the complex and real Banach algebras of all continuous
complex-valued and continuous real-valued functions on under
the uniform norm on , respectively. Recently, Fupinwong and
Dhompongsa (2010) obtained a general condition for infinite dimensional
unital commutative real and complex Banach algebras to fail the fixed-point property and showed that and are examples of such
algebras. At the same time Dhompongsa et al. (2011) showed that a complex -algebra has the fixed-point
property if and only if is finite dimensional. In this paper we show
that some complex and real unital uniformly closed subalgebras of
do not have the fixed-point property by using the results given by
them and by applying the concept of peak points for those subalgebras.