location:  Publications → journals
Search results

Search: All articles in the CJM digital archive with keyword Asplund space

 Expand all        Collapse all Results 1 - 2 of 2

1. CJM 2001 (vol 53 pp. 1174)

Loewen, Philip D.; Wang, Xianfu
 A Generalized Variational Principle We prove a strong variant of the Borwein-Preiss variational principle, and show that on Asplund spaces, Stegall's variational principle follows from it via a generalized Smulyan test. Applications are discussed. Keywords:variational principle, strong minimizer, generalized Smulyan test, Asplund space, dimple point, porosityCategory:49J52

2. CJM 1999 (vol 51 pp. 26)

Fabian, Marián; Mordukhovich, Boris S.
 Separable Reduction and Supporting Properties of FrÃ©chet-Like Normals in Banach Spaces We develop a method of separable reduction for Fr\'{e}chet-like normals and $\epsilon$-normals to arbitrary sets in general Banach spaces. This method allows us to reduce certain problems involving such normals in nonseparable spaces to the separable case. It is particularly helpful in Asplund spaces where every separable subspace admits a Fr\'{e}chet smooth renorm. As an applicaton of the separable reduction method in Asplund spaces, we provide a new direct proof of a nonconvex extension of the celebrated Bishop-Phelps density theorem. Moreover, in this way we establish new characterizations of Asplund spaces in terms of $\epsilon$-normals. Keywords:nonsmooth analysis, Banach spaces, separable reduction, FrÃ©chet-like normals and subdifferentials, supporting properties, Asplund spacesCategories:49J52, 58C20, 46B20
 top of page | contact us | privacy | site map |