The ability to unmount a file system will depend on who performed the initial mount. If a file system is specified as part of the zone's configuration using the zonecfg command, then the global zone owns this mount and the non-global zone administrator cannot unmount the file system. If the file system is mounted from within the non-global zone, for example, by specifying the mount in the zone's /etc/vfstab file, then the non-global zone administrator can unmount the file system.