Fredholm Weighted Composition Operators Between Lipschitz Algebras

Let X and Y be (not necessarily compact) metric spaces. We provide a complete description of Fredholm weighted composition operators between Lipschitz algebras Lip α ( X ) and Lip α ( Y ) for 0 < α ≤ 1 . All results and some more hold when such operators are between little Lipschitz algebras lip α ( X ) and lip α ( Y ) with 0 < α < 1 . As an application, we characterize Fredholm multiplication operators on little Lipschitz algebras and show that the Fredholm index of such operators is zero.