4 problems

Marcus's block permanent conjecture. Then

Bourin's normal-block extension of Theorem 2.5. The same inequality should hold for all normal block matrices partitioned into blocks of the same size and for all symmetric norms.…

Bourin's symmetric-norm extension of Corollary 2.2. The same inequality should hold for all symmetric norms:

Bourin's block-matrix subadditivity conjecture. This estimate should remain true with $t^p$ replaced by every non-negative concave function $f$ on $[0,\infty)$: