On the character space of Banach vector-valued function algebras

Document Type : Research Paper

Author

School of Mathematics and Computer Sciences, ‎Damghan University‎, ‎Damghan‎, ‎P.O‎. ‎Box 36715-364‎, ‎Damghan‎, ‎Iran.

Abstract

‎Given a compact space $X$ and a commutative Banach algebra‎ ‎$A$‎, ‎the character spaces of $A$-valued function algebras on $X$ are‎ ‎investigated‎. ‎The class of natural $A$-valued function algebras‎, ‎those whose characters can be described by means of characters of $A$ and‎ ‎point evaluation homomorphisms‎, ‎is introduced and studied‎. ‎For an‎ ‎admissible Banach $A$-valued function algebra $\mathscr{A}$ on $X$‎, ‎conditions under which the character space $\mathfrak{M}(\mathscr{A})$‎ ‎is homeomorphic to $\mathfrak{M}(\mathfrak{A})\times \mathfrak{M}(A)$ are presented‎, ‎where $\mathfrak{A}=C(X) \cap\mathscr{A}$‎ ‎is the subalgebra of $\mathscr{A}$ consisting of scalar-valued functions‎. ‎An illustration of the results is given by some examples.

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References

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Bulletin of the Iranian Mathematical Society
Volume 43, Issue 5
October 2017
Pages 1195-1207

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History

  • Receive Date: 02 January 2016
  • Revise Date: 12 May 2016
  • Accept Date: 13 May 2016

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