Abstract
Let T : A -> X be a bounded linear operator, where A is a C*-algebra, and X denotes an essential Banach A-bimodule. We prove that the following statements are equivalent:
(a) T is anti-derivable at zero (i.e., ab = 0 in A implies T (b)a + bT (a) = 0);
(b) There exist an anti-derivation d : A -> X ** and an element xi is an element of X ** satisfying xi a = a xi, xi[a, b] = 0, T (ab) = bT (a)+ T (b)a - b xi a, and T (a) = d(a) + xi a, for all a, b is an element of A.
We also prove a similar equivalence when X is replaced with A**. This provides a complete characterization of those bounded linear maps from A into X or into A ** which are anti-derivable at zero. We also present a complete characterization of those continuous linear operators which are *-anti-derivable at zero.