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On a new class of sequences related to the space \(\ell^p\). (English) Zbl 1005.46002
The authors define a new sequence space, which is a generalization of a space due to Sargent, and show that it is a Banach space in which the coordinate maps are continuous; furthermore it is symmetric, normal and lies between the spaces \(\ell^p\) and \(\ell^\infty\). They also give conditions implying that their new space should be identical with \(\ell^p\) or \(\ell^\infty\), respectively.

MSC:
46A45 Sequence spaces (including Köthe sequence spaces)
40A05 Convergence and divergence of series and sequences
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