Altay, Bilâl; Başar, Feyzi On the paranormed Riesz sequence spaces of non-absolute type. (English) Zbl 1058.46002 Southeast Asian Bull. Math. 26, No. 5, 701-715 (2003). Summary: The sequence space \(\ell(p)\) was defined by I. J. Maddox [Q. J. Math. Oxf. II. Ser. 18, 345–355 (1967; Zbl 0156.06602)]. In the present paper the Riesz sequence spaces \(r^q(p)\) of non-absolute type are introduce and it is proved that the spaces \(r^q(p)\) and \(\ell(p)\) are linearly isomorphic. Besides this, the \(\alpha\)-, \(\beta\)- and \(\gamma\)-duals of the spaces \(r^q(p)\) are computed and a basis of the space \(r^q(p)\) is constructed. Finally the class \((r^q(p):\mu)\) of infinite matrices is characterized for \(\mu\in\{\ell_\infty, bs,c,cs,c_0,cs_0, r^t_\infty, r^t_c,r^t_0\}\). Cited in 5 ReviewsCited in 51 Documents MSC: 46A45 Sequence spaces (including Köthe sequence spaces) 40C05 Matrix methods for summability Citations:Zbl 0156.06602 PDFBibTeX XMLCite \textit{B. Altay} and \textit{F. Başar}, Southeast Asian Bull. Math. 26, No. 5, 701--715 (2003; Zbl 1058.46002)