Is the space of Holder functions predual of L^1?

Document Type : Original Article

Author

Kharazmi University, Tehran, Iran

Abstract

Let (X,d) be a compact pointed metric space. In this paper, we investigate the condition on the underlying metric space (X,d) which implies that the little Lipschitz space on (X,d) is predual of L^1(\mu). Then, we conclude that the space of Holder functions on every compact pointed space, and for each 0<alpha<1 is not predual of L^1(\mu).

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[1] Weaver, N. (2018). Lipschitz Algebras (Second Edition). World Scientific, Singapore.