Sum and product of certain BK spaces and matrix transformations between these spaces (Q558266)

The article studies weighted Banach sequence spaces of the type \(s_\alpha = \{(x_n)_{n \in \mathbb N} \in \mathbb C^{\mathbb N}: x_n/\alpha_n \in \ell_\infty\}\) for a weight sequence \(\alpha \in (0,\infty)^{\mathbb N}\), sums and products \(s_\alpha \ast s_\beta =\{ (x_n y_n)_{n \in \mathbb N}: x\in s_\alpha, y\in s_\beta\}\), as well as matrix transforms between such spaces. Many elementary properties and relations are expressed in terms of growth conditions for the weight sequences \(\alpha\) and \(\beta\).