NONLINEAR SPECTRAL RADIUS PRESERVERS BETWEEN CERTAIN NON-UNITAL BANACH FUNCTION ALGEBRAS

Let alpha(o)is an element of C \ {0}, A and B be Banach function algebras. Also, let rho(1) : Omega(1 )-> A, rho(2) : Omega(2) -> A, tau(1 ): Omega(1 )-> B and T-2 : Omega(2 )-> B be surjections such that parallel to rho(1)(omega(1))rho(2)(omega(2)) +alpha(0)parallel to(infinity) = parallel to tau(1)(omega(1))tau(2)(omega(2)) + alpha(0)parallel to(infinity) for all omega(1 )is an element of Omega(1), omega(2 )is an element of Omega(2), where Omega(1), Omega(2) are two non-empty sets. Motivated by recent investigations on such maps between unital Banach function algebras, in this paper we characterize these maps for certain non-unital Banach function algebras including pointed Lipschitz algebras and abstract Segal algebras of the Figa-Talamanca-Herz algebras when the underlying groups are first countable. Moreover, sufficient conditions are given to guarantee such maps indue weighted composition operators.