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Kyungpook Mathematical Journal 2020; 60(1): 117-125

Published online March 31, 2020

Copyright © Kyungpook Mathematical Journal.

The Maximal Ideal Space of Extended Differentiable Lipschitz Algebras

Mohammad Ali Abolfathi∗ and Ali Ebadian

Department of Mathematics, Urmia University, P. O. Box 165, Urmia, Iran
e-mail : m.abolfathi@urmia.ac.ir and a.ebadian@urmia.ac.ir

Received: May 14, 2018; Revised: December 25, 2018; Accepted: December 26, 2018

Abstract

In this paper, we first introduce new classes of Lipschitz algebras of infinitely differentiable functions which are extensions of the standard Lipschitz algebras of infinitely differentiable functions. Then we determine the maximal ideal space of these extended algebras. Finally, we show that if X and K are uniformly regular subsets in the complex plane, then R(X,K) is natural.

Keywords: Banach function algebra, diff,erentiable Lipschitz algebras, extended Lipschitz algebra, maximal ideal space, rational functions. This work was supported by Urmia University.