Additive maps on standard operator algebras preserving invertibilities or zero divisors

Let and be standard operator algebras on infinite dimensional complex Banach spaces X and Y, respectively, and let Φ be an additive surjection from onto . We prove that if Φ is unital and preserves any one of (left, right) invertibility, (left, right) zero divisors, (left, right) topological divisors of zero, quasi-affinity, injectivity, surjectivity, range density, lower-boundedness and left (right) maximal ideals in both directions, then it has one of the following forms: isomorphism, conjugate isomorphism, anti-isomorphism and conjugate anti-isomorphism. We also show that Φ preserves zero products in both directions if and only if Φ is either an isomorphism or a conjugate isomorphism.