On The Fixed-Point Property of Unital Uniformly Closed Subalgebras of <inline-formula> <graphic file="1687-1812-2010-268450-i1.gif"/></inline-formula>
<p>Abstract</p> <p>Let <inline-formula> <graphic file="1687-1812-2010-268450-i2.gif"/></inline-formula> be a compact Hausdorff topological space and let <inline-formula> <graphic file="1687-1812-2010-268450-i3.gif"/></inline-form...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2010/268450 |
| Summary: | <p>Abstract</p> <p>Let <inline-formula> <graphic file="1687-1812-2010-268450-i2.gif"/></inline-formula> be a compact Hausdorff topological space and let <inline-formula> <graphic file="1687-1812-2010-268450-i3.gif"/></inline-formula> and <inline-formula> <graphic file="1687-1812-2010-268450-i4.gif"/></inline-formula> denote the complex and real Banach algebras of all continuous complex-valued and continuous real-valued functions on <inline-formula> <graphic file="1687-1812-2010-268450-i5.gif"/></inline-formula> under the uniform norm on <inline-formula> <graphic file="1687-1812-2010-268450-i6.gif"/></inline-formula>, 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 <inline-formula> <graphic file="1687-1812-2010-268450-i7.gif"/></inline-formula> and <inline-formula> <graphic file="1687-1812-2010-268450-i8.gif"/></inline-formula> are examples of such algebras. At the same time Dhompongsa et al. (2010) showed that a complex <inline-formula> <graphic file="1687-1812-2010-268450-i9.gif"/></inline-formula>-algebra <inline-formula> <graphic file="1687-1812-2010-268450-i10.gif"/></inline-formula> has the fixed-point property if and only if <inline-formula> <graphic file="1687-1812-2010-268450-i11.gif"/></inline-formula> is finite dimensional. In this paper we show that some complex and real unital uniformly closed subalgebras of <inline-formula> <graphic file="1687-1812-2010-268450-i12.gif"/></inline-formula> 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.</p> |
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| ISSN: | 1687-1820 1687-1812 |