Matrix transformation of \(l(p,s)\) to \(l_\infty(p)\) and \(c_0(p)\) (Q2708409)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Matrix transformation of \(l(p,s)\) to \(l_\infty(p)\) and \(c_0(p)\) |
scientific article |
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17 April 2001
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matrix transformations
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Matrix transformation of \(l(p,s)\) to \(l_\infty(p)\) and \(c_0(p)\) (English)
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Let \(p=(p_k)\) be a sequence with \(p_k>0\) \((k\in\mathbb{N})\). The authors characterize the matrix transformations \(A:l(p,s)\to X\) where \(l(p, s):= \{(x_k)\mid \sum_kk^{-s}|x_k|^{p_k} <\infty\}\) \((s\geq 0)\) and \(X\) is one of the sequence spaces \(l_\infty (p):=\{(x_k) \mid\sup_k|x_k |^{p_k} <\infty\}\) and \(c_0(p): =\{(x_k)\mid \lim_k|x_k|^{p_k} =0\}\).
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