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Let K be a compact Hausdorff space, a commutative com- plex Banach algebra with identity and ( ) the set of characters of .
In this note, we study the class of functions f : K → such that A ◦ f is continuous, where A 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 contin- uous functions relative to the weak topology σ( , ( )), are discussed.
We also provide some results on its completeness under the norm defined by |||f||| = ||Ω ◦f||∞.
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참고문헌 (4)
참고문헌 신청
R. G. Douglas / 1972 / Banach Algebra Techniques in Operator Theory / Academic Press
R. V. Kadison / 1983 / Fundamentals of the Theory of Operator Algebras. Vol. I / Academic Press
R. V. Kadison / 1986 / Fundamentals of the Theory of Operator Algebras. Vol. II / Academic Press
W. Fupinwong / 2010 / The fixed point property of unital abelian Banach algebras / Fixed Point Theory Appl 2010 : 13 ~
R. V. Kadison / 1983 / Fundamentals of the Theory of Operator Algebras. Vol. I / Academic Press
R. V. Kadison / 1986 / Fundamentals of the Theory of Operator Algebras. Vol. II / Academic Press
W. Fupinwong / 2010 / The fixed point property of unital abelian Banach algebras / Fixed Point Theory Appl 2010 : 13 ~
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