International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 52382, 12 pages
doi:10.1155/2007/52382
Multismoothness in Banach spaces
Bor-Luh Lin1
and T.S.S.R.K. Rao2
114 MacLean Hall, University of Iowa, Iowa City 52242, IA, USA
2Stat-Math Unit, Indian Statistical Institute, R. V. College P.O., Bangalore 560059, India
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.