Annals of Functional Analysis

Wide and tight spherical hulls of bounded sets in Banach spaces

Chan He, Senlin Wu, and Xinling Zhang

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Abstract

Let A be a bounded closed convex set in a Banach space. The boundaries of the wide spherical hull η(A) and the tight spherical hull θ(A) are characterized, the existence of diametral points of these three sets are discussed, and a further relation between these three sets is clarified. Moreover, a new characterization of balls is presented.

Article information

Source
Ann. Funct. Anal., Volume 7, Number 2 (2016), 290-302.

Dates
Received: 25 June 2015
Accepted: 4 August 2015
First available in Project Euclid: 21 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.afa/1458580169

Digital Object Identifier
doi:10.1215/20088752-3505890

Mathematical Reviews number (MathSciNet)
MR3476639

Zentralblatt MATH identifier
1373.46009

Subjects
Primary: 46B99: None of the above, but in this section
Secondary: 52A05: Convex sets without dimension restrictions 46B20: Geometry and structure of normed linear spaces

Keywords
complete sets completion of sets wide spherical hull tight spherical hull

Citation

He, Chan; Wu, Senlin; Zhang, Xinling. Wide and tight spherical hulls of bounded sets in Banach spaces. Ann. Funct. Anal. 7 (2016), no. 2, 290--302. doi:10.1215/20088752-3505890. https://projecteuclid.org/euclid.afa/1458580169


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References

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