Spectral preservers and approximate spectral preservers on operator algebras.

Let A and B be unital primitive Banach algebras with minimal idempotents. We prove that every surjective spectral isometry from A onto B is of the form λ Ψ where λ ∈ C with | λ | = 1 and Ψ is either an isomorphism or an anti-isomorphism from A onto B . As an application we show that, for all Banach spaces X and Y , the spectral nearisometries and the approximate spectrum-preserving maps from L ( X ) onto L ( Y ) are perturbations of actual spectral isometries and spectrum-preserving maps, respectively. [ABSTRACT FROM AUTHOR]