Let N be a nest on a Banach space X, and Alg N be the associated nest algebra. It is shown that if there exists a non-trivial element in N which is complemented in X, then D = (Ln)n∈N is a Lie higher derivation of ...Let N be a nest on a Banach space X, and Alg N be the associated nest algebra. It is shown that if there exists a non-trivial element in N which is complemented in X, then D = (Ln)n∈N is a Lie higher derivation of AlgAl if and only if each Ln has the form Ln(A) : Tn(A) + hn(A)I for all A ∈ AlgN, where (Tn)n∈N is a higher derivation and (hn)n∈N is a sequence of additive functionals satisfying hn([A,B]) = 0 for all A,B ∈ AlgN and all n ∈ N.展开更多
基金supported by NSF (10771157) of ChinaResearch Fund (2007-38) of Shanxi for Returned ScholarsFoundation of Shanxi University
文摘Let N be a nest on a Banach space X, and Alg N be the associated nest algebra. It is shown that if there exists a non-trivial element in N which is complemented in X, then D = (Ln)n∈N is a Lie higher derivation of AlgAl if and only if each Ln has the form Ln(A) : Tn(A) + hn(A)I for all A ∈ AlgN, where (Tn)n∈N is a higher derivation and (hn)n∈N is a sequence of additive functionals satisfying hn([A,B]) = 0 for all A,B ∈ AlgN and all n ∈ N.