Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
5
1 (Special Issue)
2014
01
01
Certain subalgebras of Lipschitz algebras of infinitely differentiable functions and their maximal ideal spaces
9
22
111
10.22075/ijnaa.2014.111
EN
D.
Alimohammadi
Department of Mathematics, Faculty of Science, Arak University, P. O. Box: 38156-8-8349, Arak, Iran.
F.
Nezamabadi
Department of Mathematics, Faculty of Science, Arak University, P. O. Box: 38156-8-8349, Arak, Iran.
Journal Article
2014
02
17
We study an interesting class of Banach function algebras of innitely dierentiable functions on<br />perfect, compact plane sets. These algebras were introduced by Honary and Mahyar in 1999, called<br />Lipschitz algebras of innitely dierentiable functions and denoted by Lip(X;M; ), where X is a<br />perfect, compact plane set, M = fMng1n<br />=0 is a sequence of positive numbers such that M0 = 1 and<br />(m+n)!<br />Mm+n<br /> ( m!<br />Mm<br />)( n!<br />Mn<br />) for m; n 2 N [ f0g and 2 (0; 1]. Let d = lim sup( n!<br />Mn<br />)<br />1<br />n and Xd = fz 2 C :<br />dist(z;X) dg. Let LipP;d(X;M; )[LipR;d(X;M; )] be the subalgebra of all f 2 Lip(X;M; )<br />that can be approximated by the restriction to Xd of polynomials [rational functions with poles o<br />Xd]. We show that the maximal ideal space of LipP;d(X;M; ) is cXd, the polynomially convex hull<br />of Xd, and the maximal ideal space of LipR;d(X;M; ) is Xd, for certain compact plane sets.. Using<br />some formulae from combinatorial analysis, we nd the maximal ideal space of certain subalgebras<br />of Lipschitz algebras of innitely dierentiable functions.
https://ijnaa.semnan.ac.ir/article_111_3aee2736a32d307e34b4d8bc34fafb5a.pdf