Journal of Convex Analysis 17 (2010), No. 2, 441--449
Copyright Heldermann Verlag 2010
On Moduli of Smoothness and Squareness
Antonio José Guirao
Dep. de Matemática Aplicada, Escuela Técnica Superior de Arquitectura, Universidad Politécnica, Camino de Vera, 46020 Valencia, Spain
anguisa2@mat.upv.es
Milen Ivanov
Faculty of Mathematics and Informatics, Sofia University, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria
milen@fmi.uni-sofia.bg
Sebastian Lajara
Dep. de Matemáticas, Escuela de Ingenieros Industriales, Universidad de Castilla-La Mancha, Campus Universitario, 02071 Albacete, Spain
Sebastian.Lajara@uclm.es
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.
Keywords: Modulus of smoothness, modulus of squareness.
MSC: 46B03, 46B20
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