On the Asplund Property of Locally Convex Spaces
β Scribed by Congxin Wu; Xiaomin Wang; Lixin Cheng; E.S. Lee
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 162 KB
- Volume
- 204
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Reflexive BANACH spaces and separable duals of BANAOE s p ~c e s possess the RADON-NIXODYM Property. The purpose of this paper is to extend these results to locally convex spaces. As the examples will show, these RNP-spaces include most spaces which occur frequently in Functional Analysis.
Let f be a continuous convex function on a Banach space E. This paper shows that every proper convex function g on E with g F f is generically Frechet differentiable if and only if the image of the subdifferential map Ρ¨ f of f has the RadonαNikodym property, and in this case it is equivalent to show
The connection between the approximation property and certain classes of locally convex spaces associated with the ideal B) of approximable operators will be discussed. It mill be shown that a FRECHET MOXTEL space has the approximation property iff it is a mixed @-space, or equivalently, iff its str