Resumen de Generalized skew derivations on nest algebras characterized by acting on zero products

Xiaofei Qi, Jinchuan Hou

• Let N be a nest on a Banach space X with N 2 N complemented in X whenever N.. = N, and let AlgN be the associated nest algebra. Assume that . : AlgN ! AlgN is an automorphism and � : AlgN ! AlgN is an additive map. It is shown that, if � is .-derivable at zero point (i.e., satis es �Â(A)B+.(A)�Â(B) = 0 whenever AB = 0), then there exists an additive .-derivation d : AlgN ! AlgN such that �Â(A) = d(A)+�Â(I)A for all A 2 AlgN. Moreover, by use of this result, the linear maps generalized .- derivable at zero point are also characterized