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

DOI

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
@article{10_4153_CMB_1983_018_7,
     author = {Polak, T. and Sims, Brailey},
     title = {A {Banach} {Space} which is {Fully} {2-Rotund} but not {Locally} {Uniformly} {Rotund}},
     journal = {Canadian mathematical bulletin},
     pages = {118--120},
     year = {1983},
     volume = {26},
     number = {1},
     doi = {10.4153/CMB-1983-018-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-018-7/}
}
TY  - JOUR
AU  - Polak, T.
AU  - Sims, Brailey
TI  - A Banach Space which is Fully 2-Rotund but not Locally Uniformly Rotund
JO  - Canadian mathematical bulletin
PY  - 1983
SP  - 118
EP  - 120
VL  - 26
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-018-7/
DO  - 10.4153/CMB-1983-018-7
ID  - 10_4153_CMB_1983_018_7
ER  - 
%0 Journal Article
%A Polak, T.
%A Sims, Brailey
%T A Banach Space which is Fully 2-Rotund but not Locally Uniformly Rotund
%J Canadian mathematical bulletin
%D 1983
%P 118-120
%V 26
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-018-7/
%R 10.4153/CMB-1983-018-7
%F 10_4153_CMB_1983_018_7

Cité par Sources :