The Maximal Ideal Spaces Of A Type Of Function Algebras And The Stability Of Some Maps On Hilbert C*-modules

Multiplicative linear functional is an important tool in the study of Banach alge-bras. The first part of this paper is devoted to the study of a type of Banach algebras generated by all continuous functions on a compact Hausdorff space and finitely many bounded real-valued functions with finitely many discontinuity points. Through studying multiplicative linear functionals, we determine the maximal ideal space of this type of Banach algebras. The second part of this paper is devoted to the stability of two kinds of mappings. First we use fixed point method to give conditions that can make a mapping on Hilbert C*-modules be approximated by a C*-semi-inner product. Then we introduce the notion of generalized derivations on Hilbert C*-modules and use fixed point method to give conditions that can make a mapping on left Hilbert C*-modules be approximated by a generalized derivation.