On the Dirichlet matrix operators in sequence spaces
Volume 44 / 2017
Applicationes Mathematicae 44 (2017), 185-196 MSC: 42C20, 47B99, 65T99, 65R32. DOI: 10.4064/am2328-4-2017 Published online: 7 July 2017
We study the analytic properties of certain special operators, referred to as D-matrix operators, which arise naturally from classical Dirichlet series. There are a number of incentives for this work, including the applicability of D-matrix operators to signal processing via fast computational algorithms. It was observed in a prior publication that certain types of D-matrix operators are continuous in $\ell _2$ (Sowa 2013). In this work the focus is on a complementary case that arises in relation to the special D-matrix associated with Riemann’s zeta function, and on its continuity properties in suitable Hilbert and Banach sequence spaces.