Disjointness preserving operators on complex Riesz spaces

It is proven that if E-C and F-C are complex Riesz spaces and if T is an order bounded disjointness preserving operator from E-C into F-C, then \Tz\ = \T\z\\ for all z is an element of E-C. This fundamental result of M. Meyer is;obtained by elementary means using as the main tool the functional calculus derived from the Freudenthal spectral theorem. It is also shown that if T is an order bounded disjointness preserving operator, a formula of the form Tz = sgn T(\z\).\T\(z) for all z is an element of E-C holds. It implies a polar decomposition of an order bounded disjointness preserving operator as the product of a Riesz homomorphism and an orthomorphism. Results of P. Meyer-Nieberg in this regard are generalized.