Papers

Peer-reviewed
Aug, 2017

Real-linear surjective isometries between function spaces

TOPOLOGY AND ITS APPLICATIONS
  • Kazuhiro Kawamura
  • ,
  • Takeshi Miura

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
DOI
https://doi.org/10.1016/j.topol.2017.05.002
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000404309600008&DestApp=WOS_CPL
ID information
  • DOI : 10.1016/j.topol.2017.05.002
  • ISSN : 0166-8641
  • eISSN : 1879-3207
  • Web of Science ID : WOS:000404309600008

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