Semifir structure and Bergman-type Nullstellensatz for operator-space row balls

Establish whether, for an arbitrary operator space structure E on C^d, the ring O(R·B_E^d) of NC functions uniformly bounded on r·\overline{B_E^d} for every 0<r<R is a semifir and satisfies an analogue of the analytic Bergman Nullstellensatz.

Background

The main results of the paper prove that O_d(R) (based on the row operator space structure) is a semifir and yield an analytic Bergman Nullstellensatz. The authors note their methods depend crucially on the row (or column) operator space structure.

They raise the question of whether analogous results extend to general operator space structures E, where B_E^d denotes the NC unit ball of E, which would broaden the scope of the theory beyond the specific row/column frameworks.