Some remarks on quasi-Cohen sets
Volume 89 / 2001
Colloquium Mathematicum 89 (2001), 169-178
MSC: 42A20, 42A55, 42C10, 43A46, 43A77.
DOI: 10.4064/cm89-2-2
Abstract
We are interested in Banach space geometry characterizations of quasi-Cohen sets. For example, it turns out that they are exactly the subsets $E$ of the dual of an abelian compact group $G$ such that the canonical injection $C(G)/C_{E^{\rm c}}(G)\hookrightarrow L^2_E(G)$ is a $2$-summing operator. This easily yields an extension of a result due to S. Kwapień and A. Pełczyński. We also investigate some properties of translation invariant quotients of $L^1$ which are isomorphic to subspaces of $L^1$.
