Strongly cyclic elements of certain operators in spaces of analytic functions (Q795301)

Let X be a topological vector space; \(x\in X\) is called a strongly cyclic element of an operator \(A\in L(X)\), if for every \(y\in X\) there is a commutant B of A such that \(y=Bx\) (a similar definition of a strongly cyclic vector \((x_ 0,...,x_{p-1})\in X^ p\) is introduced as well). Strongly cyclic elements and vectors of certain operators (of integration, differentiation, multiplication and division) in \(A_ R\) are characterized, where \(A_ R\) is the space of analytic functions on the disc \(\{| z|<R\}\).