Preservation of Extreme Points Mena Jurado, Juan Francisco Navarro Pascual, Juan Carlos Banach spaces Extreme operator Structure topology Funding: This work was supported by the Spanish AEI Project PGC2018-093794-B-I00/AEI/10.13039/ 501100011033 (MCIU/AEI/FEDER, UE), by Junta de Andalucía I+D+i grants P20 00255, A-FQM-484- UGR18, and FQM-185, by “María de Maeztu” Excellence Unit IMAG, reference CEX2020-001105-M funded by MCIN/AEI/10.13039/501100011033, and by the FQM-194 research group of the University of Almería. Acknowledgments: The authors would like to express their gratitude to the reviewers for their valuable comments and suggestions. 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. 2022-07-22T09:02:58Z 2022-07-22T09:02:58Z 2022-06-29 journal article Mena-Jurado, J.F.; Navarro-Pascual, J.C. Preservation of Extreme Points. Mathematics 2022, 10, 2268. [https://doi.org/10.3390/math10132268] http://hdl.handle.net/10481/76326 10.3390/math10132268 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional MDPI