Multipliers of mixed-norm sequence spaces and measures of noncompactness. II. (Q2757722)

In this paper the authors investigate the Hausdorff measure noncompactess of the operator \(T_\lambda:l^{r,s}\rightarrow l^{u,v}\)defined by \(T_\lambda\left( a\right) = \{ \lambda_n a_n \}\) (\(\lambda=\{\lambda_n\} \in l^\infty\) where \(l^{p,q}\) is the mixed norm sequence space in the cases when \(0 \leq r,u,s,v \leq \infty\). They prove also the necessary and sufficient condition for \(T_\lambda \) to be compact.