On Köthe-Toeplitz duals of certain sequence spaces and their matrix transformations. (English) Zbl 0805.46008

Summary: We define the sequence spaces \(\overline{\ell(p)}\) and \(\overline\ell_ p\) and determine the Köthe-Toeplitz duals of \(\overline{\ell(p)}\). We also obtain necessary and sufficient conditions for a matrix \(A\) to map \(\overline{\ell(p)}\) to \(\ell_ \infty\) and \(\overline{\ell(p)}\) to \(c\).


46A45 Sequence spaces (including Köthe sequence spaces)
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)