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On some new sequence spaces of non-absolute type related to the spaces \(l_p\) and \(l_{\infty}\). I. (English) Zbl 1265.46011

Summary: We introduce the sequence space \(l_p^{\lambda}\) of non-absolute type and prove that the spaces \(l_p^{\lambda}\) and \(l_p\) are linearly isomorphic for \(0<p\leq\infty\). Further, we show that \(l_p^{\lambda}\) is a \(p\)-normed space and a \(BK\)-space in the cases of \(0<p<1\) and \(1\leq p\leq \infty\), respectively. Furthermore, we derive some inclusion relations concerning the space \(l_p^{\lambda}\). Finally, we construct the basis for the space \(l_p^{\lambda}\), where \(1\leq p\leq\infty\).

MSC:

46A45 Sequence spaces (including Köthe sequence spaces)
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