© Davood Alimohammadi and Sirous Moradi. 2010
Received: 25 August 2010
Accepted: 24 December 2010
Published: 29 December 2010
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. (2010) 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.
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