On some new sequence spaces of non-absolute type related to the spaces \(\ell_p\) and \(\ell_\infty\) II
The spaces \(\ell_{p}^\lambda\) and \(\ell_{\infty}^\lambda\) of non-absolute type were introduced by the same authors in Part I [Filomat 25, No. 2, 33--51 (2011; Zbl 1265.46011)] as the spaces of all sequences whose \(\Lambda\)-transforms are in the spaces \(\ell_p\) and \(\ell_\infty\), respectively, where \(1\leq p<\infty\). The present paper is a natural continuation of the work done in that paper.NEWLINENEWLINEThe paper is divided mainly in two parts in connection with new results besides the introduction, a general description of the spaces \(\ell_{p}^\lambda\) and \(\ell_{\infty}^\lambda\), and references. In the first part, the \(\alpha\)-, \(\beta\)-, \(\gamma\)-duals of the spaces \(\ell_{p}^\lambda\) and \(\ell_{\infty}^\lambda\) are computed. In the second part, the matrix classes \((\ell_{p}^\lambda : \ell_\infty)\), \((\ell_{p}^\lambda : c)\), \((\ell_{p}^\lambda : c_0)\), \((\ell_{p}^\lambda : \ell_1)\), \((\ell_{1}^\lambda : \ell_p)\) and \((\ell_{\infty}^\lambda : \ell_p)\), where \(1\leq p<\infty\), are characterized. Further, the authors deduce a characterization of some other classes by means of a given basic lemma.
scientific article; zbMATH DE number 6057202