International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 3, Pages 441-448
Norm-preserving integral transformations
Department of Mathematics, University of Wisconsin-Oshkosh, Oshkosh 54901, Wisconsin, USA
Received 22 March 1984
Copyright © 1985 Yu Chuen Wei. 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.
In this paper we consider an integral transformation of the form , where is defined on and is defined on . The following results are proved: For an integral transformation to be norm-preserving, for almost all is only a necessary condition, where for each . For certain 's. for almost all is a necessary and sufficient condition for preserving the norm of certain . In this paper the analogous result for sum-preserving integral transformation is proved.