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

Başar, Feyzi; Sever, Yurdal

Math. J. Okayama Univ. 51, 149-157 (2009).

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)