Multipliers of mixed-norm sequence spaces and measures of noncompactness

Ivan Jovanovi\'c and Vladimir Rakocevi\'c

Abstract: Let $l^{p,q}$, $1\le p,\,q\le\infty$, be the mixed-norm sequence space. We investigate the Hausdorff measure of noncompactness of the operator $T_\lambda:l^{r,s}\mapsto l^{u,v}$, defined by the multiplier $T_\lambda(a)=\{\lambda_na_n\}$, $\lambda=\{\lambda_n\}\in l^\infty$, $a=\{a_n\}\in l^{r,s}$, and prove necessary and sufficient conditions for $T_\lambda$ to be a compact.

Classification (MSC2000): 30B10, 47B07

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