International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 6, Pages 937-948

A survey of weighted substitution operators and generalizations of Banach-stone theorem

R. K. Singh

Department of Mathematics, Faculty of Sciences, University of Jammu, Jammu 180006, India

Received 28 April 2004; Revised 2 November 2004

Copyright © 2005 R. K. Singh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The classical Banach-Stone theorem characterizes linear surjective isometries between C(K)-spaces. The main aim of this paper is to present a survey of Banach-Stone-theorem-type results between some function spaces. The weighted substitution operators play an important role in characterization of isometries, disjointness preserving operators, and lattice homomorphisms. Some open problems are given for further investigation.