On some new sequence spaces of invariant means
Generalizing previous work of \textit{G. Das} and \textit{S. K. Sahoo} [J. Math. Anal. Appl. 164, No. 2, 381-398 (1992; Zbl 0778.46011)] on the spaces \(w\), \([w]\) and \([w_1]\) of almost convergent sequences, the authors define new sequence spaces \(w_\sigma\), \([w]_\sigma\) and \([w_\sigma]\), replacing the translation mapping \(n\to n+1\) by a mapping \(\sigma\) of \(\mathbb N\) into itself and the Banach limit on \(\ell_\infty\) by a \(\sigma\)-invariant mean. Among other things, they show that a certain sublinear functional ``both dominates and generates \(\sigma\)-means'', and they derive some inclusion relations between the new sequence spaces. -- There are many (obvious) misprints.
scientific article; zbMATH DE number 1226286