Absolutely \((r,q)\)-summing operators on vector-valued function spaces
For Banach spaces $X,Y,Z$ and a tensor norm $\alpha$, every operator $U\in \mathcal{L}(Z\widehat{\otimes}_{\alpha}X,Y)$ induces an associated operator $U^{\#}\in \mathcal{L}(Z,\mathcal{L}(X,Y))$ by $(U^{\#}z)x=U(z\otimes x)$, $x\in X$ and $z\in Z$. \par The present paper studies the interplay between $U$ and $U^{\#}$ in the context of absolutely $(r,q)$-summing operators by considering the spaces $C_{p}(\Omega ,X)$ of $p$-continuous ($1\leq p\leq \infty$) functions $f$ on a compact Hausdorff space $\Omega$. The authors use tensor product theory to prove the majority of the results.
scientific article; zbMATH DE number 6816335
scientific article