Geodesic
Strongly Extreme Points and Approximation Properties
Canadian mathematical bulletin, Tome 61 (2018) no. 3, pp. 449-457

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DOI

We show that if $x$ is a strongly extreme point of a bounded closed convex subset of a Banach space and the identity has a geometrically and topologically good enough local approximation at $x$ , then $x$ is already a denting point. It turns out that such an approximation of the identity exists at any strongly extreme point of the unit ball of a Banach space with the unconditional compact approximation property. We also prove that every Banach space with a Schauder basis can be equivalently renormed to satisfy the suõcient conditions mentioned.
DOI : 10.4153/CMB-2017-067-3
Mots-clés : 46B20, 46B04, denting point, strongly extreme point, unconditional compact approximation property 
Abrahamsen, Trond A.; Hájek, Petr; Nygaard, Olav; Troyanski, Stanimir L. Strongly Extreme Points and Approximation Properties. Canadian mathematical bulletin, Tome 61 (2018) no. 3, pp. 449-457. doi: 10.4153/CMB-2017-067-3
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     title = {Strongly {Extreme} {Points} and {Approximation} {Properties}},
     journal = {Canadian mathematical bulletin},
     pages = {449--457},
     year = {2018},
     volume = {61},
     number = {3},
     doi = {10.4153/CMB-2017-067-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-067-3/}
}
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