Homomorphisms on algebras of Lipschitz functions
Volume 199 / 2010
Studia Mathematica 199 (2010), 95-106
MSC: Primary 46H10, 47B48; Secondary 47L10.
DOI: 10.4064/sm199-1-6
Abstract
We characterize a class of -homomorphisms on {\rm Lip}_*(X, \mathcal{B}(\mathcal{H})), a non-commutative Banach *-algebra of Lipschitz functions on a compact metric space and with values in \mathcal{B}(\mathcal{H}). We show that the zero map is the only multiplicative \ast -preserving linear functional on {\rm Lip}_*(X, \mathcal{B}(\mathcal{H})). We also establish the algebraic reflexivity property of a class of *-isomorphisms on {\rm Lip}_*(X, \mathcal{B}(\mathcal{H})).
