Characterization of higher derivations on CSL algebras (Q392151)

The authors of this paper investigate the conditions under which a family of linear maps on a CSL algebra is higher derivable. A~CSL algebra is an operator algebra of the form \(\mathrm{Alg}({ \mathcal L}) = \{T\in B(H): PTP = TP,\;P\in {\mathcal L}\}\), where \({\mathcal L}\) is a commutative subspace (projection) lattice on a Hilbert space \(H\). This work is motivated by the study of higher derivations on various types of algebras.NEWLINENEWLINEThe authors present a necessary and sufficient condition for higher derivable families of linear maps on CSL algebras. Additionally, they also consider the special case when a higher derivable family is automatically a higher derivation. This covers the case when \({\mathcal L}\) is a nest or, more generally, when \({\mathcal L}\) is an irreducible completely distributive commutative subspace lattice.