Proceedings of the American Mathematical Society
We use representations of a Banach algebra A to completely characterize all finite-dimensional left ideals in the dual of introverted subspaces of A* and in particular in the double dual A**. We give sufficient conditions under which such ideals always exist and are direct sums of one-dimensional left ideals.
Filali, M and Monfared, Mehdi S.. (2011). Finite-Dimensional Left Ideals in the Duals of Introverted Spaces. Proceedings of the American Mathematical Society, 139 (10), 3645-3656.