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- W2807598734 abstract "Every composition operator $C_{varphi}$ on the Lipschitz space $operatorname{Lip}_0(X)$ attains its norm. This fact is essentially known and we give in this paper a sequential characterization of the extremal functions for the norm of $C_{varphi}$ on $operatorname{Lip}_0(X)$. We also characterize the norm-attaining composition operators $C_{varphi}$ on the little Lipschitz space $operatorname{lip}_0(X)$ which separates points uniformly and identify the extremal functions for the norm of $C_{varphi}$ on $operatorname{lip}_0(X)$. We deduce that compact composition operators on $operatorname{lip}_0(X)$ are norm-attaining whenever the sphere unit of $operatorname{lip}_0(X)$ separates points uniformly. In particular, this condition is satisfied by spaces of little Lipschitz functions on Holder compact metric spaces $(X,d^{alpha})$ with $0 lt alpha lt 1$." @default.
- W2807598734 created "2018-06-13" @default.
- W2807598734 creator A5081454120 @default.
- W2807598734 date "2019-02-01" @default.
- W2807598734 modified "2023-09-26" @default.
- W2807598734 title "Norm-attaining Composition Operators on Lipschitz Spaces" @default.
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- W2807598734 doi "https://doi.org/10.11650/tjm/180508" @default.
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