Power set of some quasinilpotent weighted shifts (Q2032317)

The power set \(\Lambda(T)\) of a quasinilpotent operator \(T\) on a separable Hilbert space \(H\) was introduced by \textit{R. G. Douglas} and \textit{R. Yang} [Oper. Theory: Adv. Appl. 267, 167--183 (2018; Zbl 1454.47009)]. Several results about the power set of quasinilpotent operators \(T\) and its relation with their lattice of invariant subspaces are presented. For instance, a~quasinilpotent operator \(T\) such that \(\Lambda(T) = [0,1]\) with further interesting properties is constructed.