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
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 -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.