Orthogonality preserving linear maps on [formula omitted]-algebras with non-zero socles

Abstract

We study orthogonality preserving surjective linear maps from a unital C∗-algebra with non-zero socle A to a C∗-algebra. In particular, we prove that, when A has essential socle, every biorthogonality preserving surjective linear map T:A→B is automatically bounded and a Jordan ∗-isomorphism multiplied by an invertible element.