Dense resolvent conjecture for the Bloch–Torrey operator

Let $\mathcal B^D$ be the Bloch–Torrey operator on the periodically perforated domain, and let $\rho(\mathcal B^D)$ denote its resolvent set. Dense resolvent conjecture.

$$\overline{\rho(\mathcal B^D)}=\mathbb C.$$

The paper states that this conjecture implies the preceding spectral characterization by the fiber operators. Its status is not resolved in the supplied text and is part of the unresolved spectral analysis of this non-self-adjoint operator.