Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Modulus of smoothness
  • modulus of squareness

Mathematics Subject Classification

46B03, 46B20

Suggested citation

A. J. Guirao, M. Ivanov, S. Lajara. “On Moduli of Smoothness and Squareness.” Journal of Convex Analysis 17 (2010), No. 2, 441–449.

Copyright Heldermann Verlag 2010