Orthogonality preservers in C*-algebras, JB*-algebras and JB*-triples

We study orthogonality preserving operators between C*-algebras, JB*-algebras and JB*-triples. Let T :A E be an orthogonality preserving bounded linear operator from a C*-algebra to a JB*-triple satisfying that T**(1) = d is a von Neumann regular element. Then T(A) subset of E-2**(()r(d)), every element in T(A) and d operator commute in the JB*-algebra E-2** (r(d)), and there exists a triple homomorphism S: A -> E-2** (r(d)), such that T = L(d, r(d))S, where r(d) denotes the range tripotent of d in E**. An analogous result for A being a JB*-algebra is also obtained. When T : A B is an operator between two C*-algebras, we show that, denoting h = T**(l) then. T orthogonality preserving if and only if there exists a triple homomorphism S: A -> B** satisfying h*S(z) = S(z*)*h, hS(z*)* = S(z)h*, and T(z) = L(h . r(h)) (S(z)) = 1/2 (hr(h)*S(z)r(h)*h). This allows us to prove that a bounded linear operator between two C*-algebras is orthogonality preserving if and only if it preserves zero-triple-products. (C) 2008 Elsevier Inc. All rights reserved.