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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
##### Keywords:
absolute Köthe-Toeplitz duals; matrix transformations
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