Bulletin of the
Korean Mathematical Society BKMS

We give the characterizations of the classes of matrix transformations $(m(\phi),\ell_{p})$, $(n(\phi),\ell_{p})$ ([5, Theorem 2]), $(\ell_{p},m(\phi))$ ([5, Theorem 1]) and $(\ell_{p},n(\phi))$ for $1\le p\le\infty$, establish estimates for the norms of the bounded linear operators defined by those matrix transformations, and characterize the corresponding subclasses of compact matrix operators.

Keywords: sequence spaces, matrix transformations, compact operators, Hausdorff measure of noncompactness

MSC numbers: Primary 46B15; Secondary 46B45