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International Journal of Mathematics and Mathematical Sciences
Volume 10, Issue 3, Pages 615-619

Isometries of a function space

Department of Mathematics and Computer Science, Winston-Salem State University, Winston-Salem, North Carolina 27110, USA

Received 24 July 1984; Revised 16 February 1985

Copyright © 1987 Hindawi Publishing Corporation. 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.


It is proved here that an isometry on the subset of all positive functions of L1Lp() can be characterized by means of a function h together with a Borel measurable mapping ϕ of , thus generalizing the Banach-Lamparti theorem of Lp spaces.