| In this paper, we study anti-derivations and anti-left multipliers. For a class of alge- bras, which contain that triangular algebras, matrix algebras, embed algebras, Cuntz algebras, nest algebras, P-lattice algebras, linear transformation algebras L(X), we show that every anti- left multiplier on these algebras is zero. Let A be a zero product determined algebra and δ be a linear mapping from A into itself, satisfying that for any a,b in A, ab = 0 implies δ(b)a+bδ(a) = 0. We show that δ(x) = D(x) + δ(1)x, when D is an anti-derivation and δ(1) ∈ Z(A). |
