Hermitian operators on Banach algebras of Lipschitz functions

Fernanda Botelho, James Jamison, A. Jiménez-Vargas, Moisés Villegas-Vallecillos
2014 Proceedings of the American Mathematical Society  
For compact metric spaces (X, d), we show that the Lipschitz spaces Lip(X, d) and the little Lipschitz spaces lip(X, d α ) with 0 < α < 1, equipped with the sum norm, support only trivial hermitian operators, that is, real multiples of the identity operator.
doi:10.1090/s0002-9939-2014-12048-x fatcat:g7glsz7xq5bbhiktjqlxq2cete