Order completeness in Lipschitz algebras
The algebraic properties of Lipschitz algebras, including complex homomorphisms and ideals, have been well understood in the case when the underlying metric space is compact. It was earlier shown by the author of the reviewed paper in [Pac. J. Math. 164, No. 1, 179-193 (1994; Zbl 0797.46007)] that Lipschitz algebras are order-complete. Assuming the hypothesis of order continuity (or order closure) in place of norm continuity, the author obtains a characterization of order-continuous complex homomorphisms and order-complete subalgebras, without the usual restriction of compactness of the underlying metric space. As a corollary, it is shown that order-complete subalgebras and quotients of Lipschitz spaces by order-complete ideals are also Lipschitz spaces.
scientific article; zbMATH DE number 764041