Jordan derivations and antiderivations of generalized matrix algebras

Let be a generalized matrix algebra defined by the Morita context (A,B,_AM_B,_BN_A,Φ_MNΨ_NM). In this article we mainly study the question of whether there exist the so-called "proper" Jordan derivations for the generalized matrix algebra G. It is shown that if one of the bilinear pairings Φ_MN and Ψ_NM is nondegenerate, then every antiderivation of G is zero. Furthermore, if the bilinear pairings Φ_MN and Ψ_NM are both zero, then every Jordan derivation of G is the sum of a derivation and an antiderivation. Several constructive examples and counterexamples are presented.