2019
DOI: 10.11650/tjm/180508
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Norm-attaining Composition Operators on Lipschitz Spaces

Abstract: Every composition operator C ϕ 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 ϕ on Lip 0 (X). We also characterize the norm-attaining composition operators C ϕ on the little Lipschitz space lip 0 (X) which separates points uniformly and identify the extremal functions for the norm of C ϕ on lip 0 (X). We deduce that compact composition operators on lip 0 (X) are norm-attaining … Show more

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