A characterization of compact operators on ${\ell }^p$-spaces

Mortaza Abtahi

Let $A$ be a Banach space, $p>1$, and $1/p+1/q=1$. If a sequence $a=(a_i)$ in $A$ has a finite $p$-sum, then the operator ${\Lambda }_a:{\ell }^q\to A$, defined by $Λ_a(β)=\sum_{i=1}^\infty β_…