Norm-to-Weak Upper Semi-Continuity of the Duality and Pre-Duality Mappings |
| |
| Authors: | G Godefroy and V Indumathi |
| |
| Institution: | (1) Equipe d'Analyse, Université Paris VI, Case 186, 4, Place Jussieu, 75252 Paris Cedex 05, France;(2) Department of Mathematics, Pondicherry University, Pondicherry, 605014, India |
| |
| Abstract: | We show that when the duality map is norm-to-weak upper semi-continuous at some point of a dual space, the pre-duality map shares this property. We show that if x is a point of very smoothness of a Banach space X, it fails in general to be a point of very smoothness of the bidual X
**. This cannot happen however if the bidual X
** is a Grothendieck space. |
| |
| Keywords: | very smooth norms subdifferential maps |
| 本文献已被 SpringerLink 等数据库收录！ |
|
