Local automorphisms of real B(X).

In the paper local and 2-local *-automorphisms on real algebra B(X) of all bounded linear operators on a real Banach space are considered. In particular, 2-local *-automorphisms of real W*-algebra B(H_r) is described. Namely, it is proved that on real W*-algebra B(H_r) each *-automorphism is an inner and any 2-local *-automorphism is a *-automorphism. Moreover, it is proved that if X is a real Banach spaces and θ : B(X)→B(X) is a local automorphism, then θ is an automorphism. [ABSTRACT FROM AUTHOR]