The index of strong rotundity

Francisco Javier García-Pacheco; Francisco Javier García-Pacheco

doi:10.3934/math.20231043

AIMS Mathematics

2023, Volume 8, Issue 9: 20477-20486. doi: 10.3934/math.20231043

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The index of strong rotundity

Francisco Javier García-Pacheco ^,

Department of Mathematics, College of Engineering, University of Cadiz, Avda. de la Universidad 10, Puerto Real 11519, Spain

Received: 02 March 2023 Revised: 08 June 2023 Accepted: 13 June 2023 Published: 25 June 2023
MSC : 46B20

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.
- exposed point,
- rotund point,
- smooth point,
- Banach space,
- Hilbert space
Citation: Francisco Javier García-Pacheco. The index of strong rotundity[J]. AIMS Mathematics, 2023, 8(9): 20477-20486. doi: 10.3934/math.20231043

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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.

References

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