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International Journal of Mathematics and Mathematical Sciences
Volume 2007, Article ID 52382, 12 pages
http://dx.doi.org/10.1155/2007/52382
Research Article

Multismoothness in Banach Spaces

114 MacLean Hall, University of Iowa, Iowa City, IA 52242, USA
2Stat-Math Unit, Indian Statistical Institute, R. V. College P.O., Bangalore 560059, India

Received 3 July 2007; Accepted 18 September 2007

Academic Editor: Andrei I. Volodin

Copyright © 2007 Bor-Luh Lin and T. S. S. R. K. Rao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, motivated by the results published by R. Khalil and A. Saleh in 2005, we study the notion of k-smooth points and the notion of k-smoothness, which are dual to the notion of k-rotundity. Generalizing these notions and combining smoothness with the recently introduced notion of unitary, we study classes of Banach spaces for which the vector space, spanned by the state space corresponding to a unit vector, is a closed set.