Norming subspaces isomorphic to . 1

Norming subspaces are studied widely in the duality theory of Banach spaces. These subspaces are applied to the Borel and Baire classifications of the inverse operators. The main result of this article asserts that the dual of a Banach space X contains a norming subspace isomorphic to . 1 provided that the following two conditions are satisfied: (1) X* contains a subspace isomorphic to . 1; and (2) X* contains a separable norming subspace.