Absolute and Ordinary K{ö}the-toeplitz Duals of Some Sets of Sequences and Matrix Transformations


Eberhard Malkowsky


We determine the ordinary Köthe--Toeplitz dual of the set $\Delta l_\infty(p)$ and the absolute Köthe--Toeplitz duals of the sets $\Delta l_{\infty}(p)$, $\Delta c_0(p)$ and $\Delta c(p)$ defined by Ahmad and Mursaleen. Further we investigate matrix transformations in these spaces and give a characterization of the class $\bigl(\Delta l_\infty(p),l_\infty\bigr)$.