Annals of Functional Analysis

On the structure of the dual unit ball of strict u-ideals

Julia Martsinkevitš and Märt Põldvere

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Abstract

It is known that if a Banach space Y is a u-ideal in its bidual Y** with respect to the canonical projection on the third dual Y*** , then Y* contains “many” functionals admitting a unique norm-preserving extension to Y**—the dual unit ball BY* is the norm-closed convex hull of its weak* strongly exposed points by a result of Å. Lima from 1995. We show that if Y is a strict u-ideal in a Banach space X with respect to an ideal projection P on X* , and X/Y is separable, then BY* is the τP-closed convex hull of functionals admitting a unique norm-preserving extension to X, where τP is a certain weak topology on Y* defined by the ideal projection P.

Article information

Source
Ann. Funct. Anal., Volume 10, Number 1 (2019), 46-59.

Dates
Received: 27 October 2017
Accepted: 24 February 2018
First available in Project Euclid: 16 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.afa/1547629222

Digital Object Identifier
doi:10.1215/20088752-2018-0007

Mathematical Reviews number (MathSciNet)
MR3899955

Zentralblatt MATH identifier
07045484

Subjects
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]

Keywords
strict ideal norm-preserving extension dentability denting point

Citation

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


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References

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