# Real-linear isometries between certain subspaces of continuous functions

Open Mathematics (2013)

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

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topArya 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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