Zero product preserving maps on Banach algebras of Lipschitz functions

摘要

Let (K,d) be a non-empty, compact metric space and α∈]0,1[Let A be either lip_α(K) or Lip_α(K) and let B be a commutative unital Banach algebra. We show that every continuous linear map TA → B with the property that T(f)T(g)=0 whenever f,g∈A are such that fg=0 is of the form T=wΦ for some invertible element w in B and some continuous epimorphism Φ:A→B.