Authors

Department of Mathematics, Faculty of Science, Arak University, Arak, 38156-8-8349, Iran

Abstract

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.

Keywords

Main Subjects

[1] D. Alimohammadi and A. Ebadian, Hedberg;s theorem in real Lipschitz algebras, Indian J. Pure Appl. Math. 32 (10)(2001), 1479-1493.
 
[2] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer- Verlag, 1973.
 
[3] A. Ebadian and S. Ostadbashi, Compact homomorphisms of real Lipschitz algebras, Southeast Asian Bull. Math. 30(4) (2006), 653-661.
 
[4] A. Jimenez-Vargas and M. Villegas-Vallecillos, Compact composition operators on noncompact Lipschitz spaces, J. Math. Anal. Appl. 398(2013), 221-229.
 
[5] H. Kamowitz and S. Scheinberg, Some properties of endomorphisms of Lipschitz algebras, Studia Math. 96 (1990), 61-67.
 
[6] S. H. Kulkarni and B. V. Limaye, Gleason parts of real function algebras, Canad. J. Math. (33) (1) (1981), 181-200.
 
[7] S. H. Kulkarni and B. V. Limaye, Real Function Algebras, Marcel Dekker, New Yorke, 1992.
 
[8] D. R. Sherbert, Banach algebras of Lipschitz functions, Paci c J. Math. 13(1963), 1387-1399.
 
[9] D. R. Sherbert, The structure of ideals and point derivations of Banach algebras of Lipschitz functions, Trans. Amer. Math. Soc. 111(1964). 240-272.
 
[10] N. Weaver, Lipschitz Algebras, World Scienti c, New Jersey, 1999.