The index of strong rotundity

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URI: http://hdl.handle.net/10498/31483

DOI: 10.3934/MATH.20231043

ISSN: 2473-6988

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Author/s
García Pacheco, Francisco JavierAuthority UCA
Date
2023
Department
Matemáticas
Source
AIMS Mathematics - 2023, Vol. 8 n. 9 pp. 20477-20486
Abstract
The index of strong rotundity is introduced. This index is used to determine how far an element of the unit sphere of a real Banach space is from being a strongly exposed point of the unit ball. This index is computed for Hilbert spaces. Characterizations of the set of rotund points and the set of smooth points are provided for a better understanding of the construction of the index of strong rotundity. Finally, applications to the stereographic projection are provided
Subjects
exposed point; rotund point; smooth point; Banach space; Hilbert space
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