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Let  Open image in new window  be a compact Hausdorff topological space and let  Open image in new window  and  Open image in new window  denote the complex and real Banach algebras of all continuous complex-valued and continuous real-valued functions on  Open image in new window  under the uniform norm on  Open image in new window , 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  Open image in new window  and  Open image in new window  are examples of such algebras. At the same time Dhompongsa et al. (2010) showed that a complex  Open image in new window -algebra  Open image in new window  has the fixed-point property if and only if  Open image in new window  is finite dimensional. In this paper we show that some complex and real unital uniformly closed subalgebras of  Open image in new window  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.

On The Fixed-Point Property of Unital Uniformly Closed Subalgebras of "Equation missing"