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 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.
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MH and JJF contributed equally to this work. Both authors participated in the conception and design of the work equally.
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This work was partially supported by a grant from the IMU-CDC. J.J. Font was supported by Spanish Government grant AEI Project PID2019-106529GB-I00 / AEI / 10.13039/501100011033.
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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/s13324-024-00894-2
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DOI: https://doi.org/10.1007/s13324-024-00894-2