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On the domain of the triangle \(A(\lambda)\) on the spaces of null, convergent, and bounded sequences. (English) Zbl 1303.40003

Summary: We introduce the spaces of \(A(\lambda)\)-null, \(A(\lambda)\)-convergent, and \(A(\lambda)\)-bounded sequences. We examine some topological properties of the spaces and give some inclusion relations concerning these sequence spaces. Furthermore, we compute \(\alpha\)-, \(\beta\)-, and \(\gamma\)-duals of these spaces. Finally, we characterize some classes of matrix transformations from the spaces of \(A(\lambda)\)-bounded and \(A(\lambda)\)-convergent sequences to the spaces of bounded, almost convergent, almost null, and convergent sequences and present a Steinhaus type theorem.

MSC:

40C05 Matrix methods for summability
46A45 Sequence spaces (including Köthe sequence spaces)
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