International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 4, Pages 677-680
doi:10.1155/S016117129500086X

A note on finite codimensional linear isometries of C(X) into C(Y)

Sin-Ei Takahasi1 and Takateru Okayasu2

1Department of Basic Technology, Applied Mathematics and Physics, Yamagata University, Yomezawa 992, Japan
2Department of Mathematics, Faculty of Science, Yamagata University, Yamagata 990, Japan

Received 24 April 1994; Revised 25 May 1995

Copyright © 1995 Sin-Ei Takahasi and Takateru Okayasu. 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.

Abstract

Let (X,Y) be a pair of compact Hausdorff spaces. It is shown that a certain property of the class of continuous maps of Y onto X is equivalent to the non-existence of linear isometry of C(X) into C(Y) whose range has finite codimension >0.