Real-linear isometries between certain subspaces of continuous functions

Arya Jamshidi; Fereshteh Sady

Open Mathematics (2013)

  • Volume: 11, Issue: 11, page 2034-2043
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Arya Jamshidi, and Fereshteh Sady. "Real-linear isometries between certain subspaces of continuous functions." Open Mathematics 11.11 (2013): 2034-2043. <http://eudml.org/doc/269081>.

@article{AryaJamshidi2013,
abstract = {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.},
author = {Arya Jamshidi, Fereshteh Sady},
journal = {Open Mathematics},
keywords = {Real-linear isometry; Function space; Uniform algebra; Choquet boundary; Lipschitz space; real-linear isometry; function space; uniform algebra; boundary},
language = {eng},
number = {11},
pages = {2034-2043},
title = {Real-linear isometries between certain subspaces of continuous functions},
url = {http://eudml.org/doc/269081},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Arya Jamshidi
AU - Fereshteh Sady
TI - Real-linear isometries between certain subspaces of continuous functions
JO - Open Mathematics
PY - 2013
VL - 11
IS - 11
SP - 2034
EP - 2043
AB - 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.
LA - eng
KW - Real-linear isometry; Function space; Uniform algebra; Choquet boundary; Lipschitz space; real-linear isometry; function space; uniform algebra; boundary
UR - http://eudml.org/doc/269081
ER -

References

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