Mursaleen, M.; Noman, Abdullah K. On some new sequence spaces of non-absolute type related to the spaces \(l_p\) and \(l_{\infty}\). I. (English) Zbl 1265.46011 Filomat 25, No. 2, 33-51 (2011). Summary: We introduce the sequence space \(l_p^{\lambda}\) of non-absolute type and prove that the spaces \(l_p^{\lambda}\) and \(l_p\) are linearly isomorphic for \(0<p\leq\infty\). Further, we show that \(l_p^{\lambda}\) is a \(p\)-normed space and a \(BK\)-space in the cases of \(0<p<1\) and \(1\leq p\leq \infty\), respectively. Furthermore, we derive some inclusion relations concerning the space \(l_p^{\lambda}\). Finally, we construct the basis for the space \(l_p^{\lambda}\), where \(1\leq p\leq\infty\). Cited in 1 ReviewCited in 43 Documents MSC: 46A45 Sequence spaces (including Köthe sequence spaces) Keywords:BK-space; Schauder basis; matrix mapping PDFBibTeX XMLCite \textit{M. Mursaleen} and \textit{A. K. Noman}, Filomat 25, No. 2, 33--51 (2011; Zbl 1265.46011) Full Text: DOI