Hermitian operators on Banach algebras of Lipschitz functions

Botelho, Fernanda; Jamison, James; Jiménez-Vargas, A.; Villegas-Vallecillos, Moisés

doi:10.1090/S0002-9939-2014-12048-X

Hermitian operators on Banach algebras of Lipschitz functions
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by Fernanda Botelho, James Jamison, A. Jiménez-Vargas and Moisés Villegas-Vallecillos PDF

Proc. Amer. Math. Soc. 142 (2014), 3469-3481 Request permission

Abstract:

For compact metric spaces $(X,d)$, we show that the Lipschitz spaces $\mathrm {Lip}(X,d)$ and the little Lipschitz spaces $\mathrm {lip}(X,d^\alpha )$ with $0<\alpha <1,$ equipped with the sum norm, support only trivial hermitian operators, that is, real multiples of the identity operator.

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