In this paper we first consider a real-linear isometry T from a certain subspace A of C(X) (endowed with supremum norm) into C(Y) where X and Y are compact Hausdorff spaces and give a result concerning the description of T whenever A is a uniform algebra on X. The result is improved for the case where T(A) is, in addition, a complex subspace of C(Y). We also give a similar description for the case where A is a function space on X and the range of T is a real subspace of C(Y) satisfying a ceratin separating property. Next similar results are obtained for real-linear isometries between spaces of Lipschitz functions on compact metric spaces endowed with a certain complete norm.
@article{bwmeta1.element.doi-10_2478_s11533-013-0303-z,
author = {Arya Jamshidi and Fereshteh Sady},
title = {Real-linear isometries between certain subspaces of continuous functions},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {2034-2043},
zbl = {1294.46043},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0303-z}
}
Arya Jamshidi; Fereshteh Sady. Real-linear isometries between certain subspaces of continuous functions. Open Mathematics, Tome 11 (2013) pp. 2034-2043. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0303-z/
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