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Matrix maps on sequence spaces associated with sets of integers. (English) Zbl 0843.47017

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 \(\ell_\infty\).

MSC:

47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
46A45 Sequence spaces (including Köthe sequence spaces)
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