On the classical paranormed sequence spaces and related duals over the non-Newtonian complex field
Summary: The studies on sequence spaces were extended by using the notion of associated multiplier sequences. A multiplier sequence can be used to accelerate the convergence of the sequences in some spaces. In some sense, it can be viewed as a catalyst, which is used to accelerate the process of chemical reaction. Sometimes the associated multiplier sequence delays the rate of convergence of a sequence. In the present paper, the classical paranormed sequence spaces are introduced and it is proved that the spaces are \(\star\)-complete. By using the notion of multiplier sequence, the \(\alpha\)-, \(\beta\)-, and \(\gamma\)-duals of certain paranormed spaces are computed and their bases are constructed.
scientific article; zbMATH DE number 6499104
scientific article