Surjective isometries on function spaces with derivatives

2025/03/07 by Cabrera-Padilla, M. G., Jiménez-Vargas, A., Miura, Takeshi +1
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2503.05097

Abstract

Let A be a complex Banach space with a norm ‖f‖=‖f‖_X+‖d(f)‖_Y for f∈ A, where d is a complex linear map from A onto a Banach space B, and ‖⋅‖_K represents the supremum norm on a compact Hausdorff space K. In this paper, we characterize surjective isometries on (A,‖⋅‖), which may be nonlinear. This unifies former results on surjective isometries between specific function spaces.

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