Isometries of absolutely continuous function spaces with respect to the sum-norm
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Title
Isometries of absolutely continuous function spaces with respect to the sum-normDate
2024-03-26Publisher
SpringerISSN
1664-2368; 1664-235XBibliographic citation
Hosseini, M., Font, J.J. Isometries of absolutely continuous function spaces with respect to the sum-norm. Anal.Math.Phys. 14, 36 (2024). https://doi.org/10.1007/s13324-024-00894-2Type
info:eu-repo/semantics/bookPublisher version
https://link.springer.com/article/10.1007/s13324-024-00894-2Version
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Abstract
In this paper we give a complete description of surjective linear isometries between Banach spaces of absolutely continuous functions on arbitrary (not necessarily compact) subsets of the real line with respect to the ... [+]
In this paper we give a complete description of surjective linear isometries between Banach spaces of absolutely continuous functions on arbitrary (not necessarily compact) subsets of the real line with respect to the sum-norm. We also use this description to study approximate local isometries and approximate 2-local isometries on these spaces. In particular, we present generalizations of all known results concerning such isometries, and obtain the reflexivity and 2-reflexivity of the isometry group of absolutely continuous function spaces in a noncompact framework. [-]
Description
This version of the article has been accepted for publication, after peer review and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, ... [+]
This version of the article has been accepted for publication, after peer review and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s13324-024-00894-2 [-]
Is part of
Analysis and Mathematical Physics, 2024, vol. 14, no 2Funder Name
Ministerio de Ciencia, Innovación y Universidades | IMU-CDC
Funder ID
http://dx.doi.org/10.13039/501100011033
Project code
MICIU/ICTI2017-2020/PID2019-106529GB-I00
Project title or grant
Álgebras de funciones sobre grupos topológicos
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© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024
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http://rightsstatements.org/vocab/CNE/1.0/
info:eu-repo/semantics/embargoedAccess
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