Norm-attaining composition operators on Lipschitz spaces
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Jiménez Vargas, AntonioDate
2028-05-28Abstract
Every composition operator C_{\varphi} on the Lipschitz space 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 Lip_0(X). We also characterize the norm-attaining composition operators C_{\varphi} on the little Lipschitz space lip_0(X) which separates points uniformly and identify the extremal functions for the norm of C_{\varphi} on lip_0(X). We deduce that compact composition operators on lip_0(X) are
norm-attaining whenever the sphere unit of lip_0(X) separates points uniformly. In particular, this condition is satisfi ed by spaces of little Lipschitz functions on Hölder compact metric spaces (X,d^{\alpha}) with 0<\alpha<1.
Palabra/s clave
Composition operator
Compact operator
Norm-attaining operator
Lipschitz function
Little Lipschitz function