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February 2019 On the structure of the dual unit ball of strict u-ideals
Julia Martsinkevitš, Märt Põldvere
Ann. Funct. Anal. 10(1): 46-59 (February 2019). DOI: 10.1215/20088752-2018-0007

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.

Citation

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Julia Martsinkevitš. Märt Põldvere. "On the structure of the dual unit ball of strict u-ideals." Ann. Funct. Anal. 10 (1) 46 - 59, February 2019. https://doi.org/10.1215/20088752-2018-0007

Information

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

zbMATH: 07045484
MathSciNet: MR3899955
Digital Object Identifier: 10.1215/20088752-2018-0007

Subjects:
Primary: 46B20
Secondary: 46A55, 46B22

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.10 • No. 1 • February 2019
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