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

Autores: Xiaofei Qi, Jinchuan Hou
Localización: Publicationes Mathematicae Debrecen, ISSN 0033-3883, Tomus 78, Fasc. 2, 2011, págs. 457-468
Idioma: inglés
DOI: 10.5486/pmd.2011.4831
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Resumen
- 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 �Â : AlgN ! AlgN is an additive map. It is shown that, if �Â 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