Uniform Convexity and the Bishop–Phelps–Bollobás Property
Canadian journal of mathematics, Tome 66 (2014) no. 2, pp. 373-386
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A new characterization of the uniform convexity of Banach space is obtained in the sense of the Bishop–Phelps–Bollobás theorem. It is also proved that the couple of Banach spaces $\left( X,Y \right)$ has the Bishop–Phelps–Bollobás property for every Banach space $Y$ when $X$ is uniformly convex. As a corollary, we show that the Bishop–Phelps–Bollobás theorem holds for bilinear forms on ${{\ell }_{p}}\,\times \,{{\ell }_{q}}$ $\left( 1\, .
Mots-clés :
46B20, 46B22, Bishop–Phelps–Bollobás property, Bishop–Phelps–Bollobás theorem, norm attaining, uniformly convex
Kim, Sun Kwang; Lee, Han Ju. Uniform Convexity and the Bishop–Phelps–Bollobás Property. Canadian journal of mathematics, Tome 66 (2014) no. 2, pp. 373-386. doi: 10.4153/CJM-2013-009-2
@article{10_4153_CJM_2013_009_2,
author = {Kim, Sun Kwang and Lee, Han Ju},
title = {Uniform {Convexity} and the {Bishop{\textendash}Phelps{\textendash}Bollob\'as} {Property}},
journal = {Canadian journal of mathematics},
pages = {373--386},
year = {2014},
volume = {66},
number = {2},
doi = {10.4153/CJM-2013-009-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2013-009-2/}
}
TY - JOUR AU - Kim, Sun Kwang AU - Lee, Han Ju TI - Uniform Convexity and the Bishop–Phelps–Bollobás Property JO - Canadian journal of mathematics PY - 2014 SP - 373 EP - 386 VL - 66 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2013-009-2/ DO - 10.4153/CJM-2013-009-2 ID - 10_4153_CJM_2013_009_2 ER -
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