Alessandro Costa

The weak maximizing property is not inherited by subspaces of the domain

We construct a separable reflexive Banach lattice $X$ and a closed sublattice $E\subseteq X$ such that every bounded linear operator from $X$ into $\ell_2$ is compact, whereas there exists a positive operator from $E$ into $\ell_2$ that does not attain its norm and admits a positive maximizing sequence converging weakl...