Dust 514 and Eve Online were always pitched as complementary experiences, and the two games are slowly coalescing. The next update to Dust 514 will further the shared experience by making Corporations work across both platforms.
A post on the PlayStation Blog details the update, which will let you join and manage Corporations on PC with EVE or PlayStation 3 with Dust. You can take control as a CEO or director of a Corporation in either game, which includes designing a logo, assigning roles, taking part in real-time battles, and accepting new members.
EVE players will also see Dust player's portraits, and vice-versa. Some aspects of Corporation management will still be kept on EVE Online, at least for the time being, but the blog promises you can use EVE to appoint a director in Dust.