Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 10, Number 1 (2019), 46-59.
On the structure of the dual unit ball of strict -ideals
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 .
Ann. Funct. Anal., Volume 10, Number 1 (2019), 46-59.
Received: 27 October 2017
Accepted: 24 February 2018
First available in Project Euclid: 16 January 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46B20: Geometry and structure of normed linear spaces
Secondary: 46A55: Convex sets in topological linear spaces; Choquet theory [See also 52A07] 46B22: Radon-Nikodým, Kreĭn-Milman and related properties [See also 46G10]
Martsinkevitš, Julia; Põldvere, Märt. On the structure of the dual unit ball of strict $u$ -ideals. Ann. Funct. Anal. 10 (2019), no. 1, 46--59. doi:10.1215/20088752-2018-0007. https://projecteuclid.org/euclid.afa/1547629222