2-local Jordan automorphisms on operator algebras

We investigate 2-local Jordan automorphisms on operator algebras. In particular, we show that every 2-local Jordan automorphism of the algebra of all n x n real or complex matrices is either an automorphism or an anti-automorphism. The same is true for 2-local Jordan automorphisms of any subalgebra of B(X) which contains the ideal of all compact operators on X, where X is a real or complex separable Banach spaces and B(X) is the algebra of all bounded linear operators on X.