Geodesic
A Banach Space which is Fully 2-Rotund but not Locally Uniformly Rotund
Canadian mathematical bulletin, Tome 26 (1983) no. 1, pp. 118-120

Voir la notice de l'article provenant de la source Cambridge University Press

A Banach space is fully 2-rotund if (x n ) converges whenever ‖x n + x m ‖ converges as m, n → ∞ and locally uniformly rotund if x n → x whenever ‖x n ‖ and ‖(x n + x)/2‖ → ‖x‖.We show that I 2 with the equivalent norm is fully 2-rotund but not locally uniformly rotund, thus answering in the negative a question first raised by Fan and Glicksberg in 1958.
DOI : 10.4153/CMB-1983-018-7
Mots-clés : 46B20 
Polak, T.; Sims, Brailey. A Banach Space which is Fully 2-Rotund but not Locally Uniformly Rotund. Canadian mathematical bulletin, Tome 26 (1983) no. 1, pp. 118-120. doi: 10.4153/CMB-1983-018-7
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