Geodesic
On Moduli of Smoothness and Squareness
Journal of convex analysis, Tome 17 (2010) no. 2, pp. 441-449

Voir la notice de l'article provenant de la source Heldermann Verlag

We study the possible equivalence classes of the moduli of smoothness of finite-dimensional Banach spaces. We show that these can be arbitrary subject to Figiel condition and, moreover, they can be realised via Orlicz spaces. Some dimension dependencies are also studied. As an application we answer in negative an open question concerning the modulus of squareness.
Classification : 46B03, 46B20
Mots-clés : Modulus of smoothness, modulus of squareness 
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     author = {A. J. Guirao and M. Ivanov and S. Lajara},
     title = {On {Moduli} of {Smoothness} and {Squareness}},
     journal = {Journal of convex analysis},
     pages = {441--449},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2010},
     url = {http://geodesic.mathdoc.fr/item/JCA_2010_17_2_JCA_2010_17_2_a5/}
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A. J. Guirao; M. Ivanov; S. Lajara. On Moduli of Smoothness and Squareness. Journal of convex analysis, Tome 17 (2010) no. 2, pp. 441-449. http://geodesic.mathdoc.fr/item/JCA_2010_17_2_JCA_2010_17_2_a5/