Anti-derivable linear maps at zero on standard operator algebras.

Let X be a complex Banach space with dim X ≥ 2 , and A ⊆ B (X) be a standard operator algebra. We show that a linear mapping δ : A → A is anti-derivable at zero (i.e., x y = 0 in A implies y δ (x) + δ (y) x = 0 ) if and only if δ = 0 . [ABSTRACT FROM AUTHOR]