Conditions for linear equivalence of operators with lower-triangular matrices (Q1072080)

Let \(A_ R\) denote the space of all singlevalued analytic functions in the disc \(K_ R=\{z: | z| <R\}\), \(R>0\), with the topology of compact convergence. Two linear operators J and A having, respectively, diagonal and lower triangular matrices are considered in \(A_ R\). In the present note the author obtains necessary conditions for the equivalence in \(A_ R\) of the operators \(J+A\) and J.