Rath, D.; Tripathy, B. C. Matrix maps on sequence spaces associated with sets of integers. (English) Zbl 0843.47017 Indian J. Pure Appl. Math. 27, No. 2, 197-206 (1996). Summary: Generalizing the space of statistically convergent sequences the space \(c_\Phi\) is introduced, where \(\Phi\) is a nonempty family of subsets of natural numbers. The matrix classes \((\ell_\infty \cap c_\Phi, c)\) and \((c_\Phi\cap \ell_\infty, m(\phi))\) are characterized which include a number of known results. Further, the classes \((w(p), X)\), \((\ell(p), X)\) and \((c, X)\) are characterized for any closed subspace \(X\) of \(\ell_\infty\). Cited in 35 Documents MSC: 47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 46A45 Sequence spaces (including Köthe sequence spaces) Keywords:space of statistically convergent sequence; matrix classes PDFBibTeX XMLCite \textit{D. Rath} and \textit{B. C. Tripathy}, Indian J. Pure Appl. Math. 27, No. 2, 197--206 (1996; Zbl 0843.47017)