Han, Deguang Continuity and linearity of additive derivations of nest algebras on Banach spaces. (English) Zbl 0856.47028 Chin. Ann. Math., Ser. B 17, No. 2, 227-236 (1996). Summary: This paper discusses the problem concerning the continuity and linearity of additive derivations of nest algebras on normed spaces. It is proved that every linear derivation of a nest algebra \(\text{alg } {\mathcal N}\) is continuous provided that one of the following conditions is satisfied:(1) \(0_+\supset 0\),(2) \(X_-\subset X\),(3) there exists a nontrivial idempotent \(p\) in \(\text{alg }{\mathcal N}\) such that the range of \(p\) belongs to \(\mathcal N\).It is also proved that every additive derivation of a nest algebra is automatically linear if the underlying normed space is infinite-dimensional. Cited in 8 Documents MSC: 47L30 Abstract operator algebras on Hilbert spaces 47B47 Commutators, derivations, elementary operators, etc. Keywords:continuity; linearity; additive derivations; nest algebras PDFBibTeX XMLCite \textit{D. Han}, Chin. Ann. Math., Ser. B 17, No. 2, 227--236 (1996; Zbl 0856.47028)