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Matrix transformations between the sequence spaces of Maddox. (English) Zbl 0791.47029

Summary: The sequence spaces of Maddox \(\ell(p)\), \(c_ 0(p)\), \(c(p)\), and \(\ell_ \infty(p)\), with a sequence \(p=(p_ k)\) as parameter, generalise the classical sequence spaces \(\ell_ 1\), \(c_ 0\), \(c\), and \(\ell_ \infty\). In this paper, Toeplitz conditions are derived for matrices to map a Maddox sequence space into another such space.

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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