On The Fixed-Point Property of Unital Uniformly Closed Subalgebras of
Fixed Point Theory and Applications volume 2010, Article number: 268450 (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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Alimohammadi, D., Moradi, S. On The Fixed-Point Property of Unital Uniformly Closed Subalgebras of . Fixed Point Theory Appl 2010, 268450 (2010). https://doi.org/10.1155/2010/268450