Aug, 2017
Real-linear surjective isometries between function spaces
TOPOLOGY AND ITS APPLICATIONS
- ,
- Volume
- 226
- Number
- First page
- 66
- Last page
- 85
- Language
- English
- Publishing type
- Research paper (scientific journal)
- DOI
- 10.1016/j.topol.2017.05.002
- Publisher
- ELSEVIER SCIENCE BV
We study surjective isometries between subspaces of continuous functions containing all constant functions and separating the points of the underlying spaces. In many contexts, every such isometry is represented by a combination of a weighted composition operator and its complex conjugate, called the canonical form, while there exists an isometry which does not take such a form ([14]). We seek a topological condition on compact Hausdorff spaces such that every surjective isometry on function spaces over the spaces has the canonical form. Also we extend the construction of [14] to show that, if a compact metrizable space X admits a semi free action of the circle group with a global section, then there exists an isometry of a function space on X which does not take the canonical form. (C) 2017 Elsevier B.V. All rights reserved.
- Link information
- ID information
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- DOI : 10.1016/j.topol.2017.05.002
- ISSN : 0166-8641
- eISSN : 1879-3207
- Web of Science ID : WOS:000404309600008