## 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)