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Absolute and ordinary Köthe-Toeplitz duals of some sets of sequences and matrix transformations. (English) Zbl 0729.46003
Summary: We determine the ordinary Köthe-Toeplitz dual of the set \(\Delta \ell_{\infty}(p)\) and the absolute Köthe-Toeplitz duals of the sets \(\Delta \ell_{\infty}(p)\), \(\Delta c_ 0(p)\) and \(\Delta\) c(p) defined by Ahmad and Mursaleen. Further we investigate matrix transformations in these spaces and give a characterization of the class \((\Delta \ell_{\infty}(p),\ell_{\infty})\).

MSC:
46A45 Sequence spaces (including Köthe sequence spaces)
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
40H05 Functional analytic methods in summability
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