3 problems

Norm-attainment correspondence conjecture. The functional $x^*$ attains its norm if and only if the lattice homomorphism $\widehat{x^*}$ attains its norm.

Let $E$ be a Banach space and let $1{\leqslant} p<\infty$. Write $\operatorname{FBL}^p[E]$ for the free Banach lattice associated with $E$, and let $I_{w^*}[E]$ be the correspondin…

Norm-attainment equivalence conjecture. One has