CONTINUITY OF BANACH ALGEBRA VALUED FUNCTIONS Rakbud, Jittisak;
Let K be a compact Hausdorff space, a commutative complex Banach algebra with identity and the set of characters of . In this note, we study the class of functions such that is continuous, where denotes the Gelfand representation of . The inclusion relations between this class, the class of continuous functions, the class of bounded functions and the class of weakly continuous functions relative to the weak topology , are discussed. We also provide some results on its completeness under the norm defined by .
Banach algebra;Gelfand representation;character;
R. G. Douglas, Banach Algebra Techniques in Operator Theory, Academic Press, New York, 1972.
W. Fupinwong and S. Dhompongsa, The fixed point property of unital abelian Banach algebras, Fixed Point Theory Appl. 2010 (2010), Artical ID 362829, 13 pp.
R. V. Kadison and J. R. Ringrose, Fundamentals of the Theory of Operator Algebras. Vol. I, Academic Press, New York, 1983.
R. V. Kadison and J. R. Ringrose, Fundamentals of the Theory of Operator Algebras. Vol. II, Academic Press, New York, 1986.