Weakly compact orthogonality preservers on C*-algebras

Abstract

We establish a complete description of weakly compact orthogonality preserving operators from a C * -algebra A (or a JB * -algebra) to a JB * -triple E. We prove that any such operator is the sum of a series of mutually orthogonal triple homomorphisms from A * * to a certain Peirce-2 subspace of E * * multiplied by a mutually orthogonal norm-null sequence in E which enjoy certain operator commutativity relations.