Additive maps preserving the minimum and surjectivity moduli of operators

Abstract.

Let ${\mathcal{H}}$ be a complex Hilbert space and let ${\mathcal{L}}({\mathcal{H}})$ be the algebra of all bounded linear operators on ${\mathcal{H}}$. We characterize additive maps from ${\mathcal{L}}({\mathcal{H}})$ onto itself preserving different spectral quantities such as the minimum modulus, the surjectivity modulus, and the maximum modulus of operators.