In this paper we consider the problem of the non-empty intersection of exposed faces in a Banach space. We find a sufficient condition to assure that the non-empty intersection of exposed faces is an exposed face. This condition involves the concept of inner point. Finally, we also prove that every minimal face of the unit ball must be an extreme point and show that this is not the case at all for minimal exposed faces since we prove that every Banach space with dimension greater than or equal to 2 can be equivalently renormed to have a non-singleton, minimal exposed face.
The author wants to thank the referee for his valuable comments and suggestions.
"On minimal exposed faces." Ark. Mat. 49 (2) 325 - 333, October 2011. https://doi.org/10.1007/s11512-010-0123-3