2-local Lie isomorphisms of operator algebras on Banach spaces

摘要

Let X and Y be complex Banach spaces of dimension greater than 2. We show that every 2-local Lie isomorphism phi of B (X) onto B (Y) has the form phi = phi + tau, where phi is an isomorphism or the negative of an anti-isomorphism of B (X) onto B (Y), and tau is a homogeneous map from B (X) into C I vanishing on all finite sums of commutators.