It is known that if a Banach space is a -ideal in its bidual with respect to the canonical projection on the third dual , then contains “many” functionals admitting a unique norm-preserving extension to —the dual unit ball is the norm-closed convex hull of its weak strongly exposed points by a result of Å. Lima from 1995. We show that if is a strict -ideal in a Banach space with respect to an ideal projection on , and is separable, then is the -closed convex hull of functionals admitting a unique norm-preserving extension to , where is a certain weak topology on defined by the ideal projection .
"On the structure of the dual unit ball of strict -ideals." Ann. Funct. Anal. 10 (1) 46 - 59, February 2019. https://doi.org/10.1215/20088752-2018-0007