Preservation of Extreme Points

Mena Jurado, Juan Francisco; Navarro Pascual, Juan Carlos

doi:10.3390/math10132268

mathematics-10-02268.pdf (220.8Ko)

Identificadores

URI: http://hdl.handle.net/10481/76326

DOI: 10.3390/math10132268

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Editorial

MDPI

Materia

Banach spaces

Extreme operator

Structure topology

Date

2022-06-29

Referencia bibliográfica

Mena-Jurado, J.F.; Navarro-Pascual, J.C. Preservation of Extreme Points. Mathematics 2022, 10, 2268. [https://doi.org/10.3390/math10132268]

Patrocinador

Junta de Andalucía I+D+i A-FQM-484-UGR18, FQM-185, MCIN/AEI/10.13039/501100011033, P20 00255; Universidad de Almería

Résumé

We characterize the extreme points of the closed unit ball of the dual of a Banach space which are preserved by the adjoint of any extreme operator. The result is related to the structure topology introduced by Alfsen and Effros on the set of all extreme points in the dual of any Banach space. As a consequence, we prove that c0(I) is the only Banach space such that the adjoint of every extreme operator taking values into it preserves extreme points.

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