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The space \(\mathcal{L}_q\) of double sequences. (English) Zbl 1168.46300

From the summary: We introduce the Banach space \({\mathcal L}_q\) of double sequences corresponding to the well-known space \(\ell_q\) of single sequences and examine some properties of the space \({\mathcal L}_q\). Furthermore, we determine the \(\beta(\upsilon)\)-dual of the space and establish that the \(\alpha\)- and \(\gamma\)-duals of the space \({\mathcal L}_q\) coincide with the \(\beta(\upsilon)\)-dual, where \(1\leq q<1\) and \(\upsilon\in\{p,bp,r\}\).

MSC:

46A45 Sequence spaces (including Köthe sequence spaces)
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