Asplund spaces, the Radon-Nikodym property and optimization

1989 ◽  
pp. 72-89
Author(s):  
Robert R. Phelps
Keyword(s):  
Asplund Spaces ◽  
Nikodym Property

scholarly journals On the characterisation of Asplund spaces

1982 ◽  
Vol 32 (1) ◽  
pp. 134-144 ◽  
Author(s):  
J. R. Giles
Keyword(s):  
Banach Space ◽  
Direct Proof ◽  
Asplund Space ◽  
Open Convex ◽  
Asplund Spaces ◽  
Separable Subspace ◽  
Nikodym Property ◽  
Continuous Convex Function ◽  
Fréchet Differentiable ◽  
Open Convex Subset

AbstractA Banach space is an Asplund space if every continuous convex function on an open convex subset is Fréchet differentiable on a dense G8 subset of its domain. The recent research on the Radon-Nikodým property in Banach spaces has revealed that a Banach space is an Asplund space if and only if every separable subspace has separable dual. It would appear that there is a case for providing a more direct proof of this characterisation.

Slicings, Selections and Their Applications

1992 ◽  
Vol 44 (3) ◽  
pp. 483-504 ◽  
Author(s):  
N. Ghoussoub ◽  
B. Maurey ◽  
W. Schachermayer
Keyword(s):  
Banach Spaces ◽  
List Type ◽  
Space Theory ◽  
Reflexive Banach Spaces ◽  
Open Problems ◽  
Infinite Dimensional ◽  
The Past ◽  
Asplund Spaces ◽  
Infinite Dimensional Banach Space ◽  
Nikodym Property

In the past few years, much progress have been made on several open problems in infinite dimensional Banach space theory. Here are some of the most recent results:1)The existence of boundedly complete basic sequences in a large class of Banach spaces including the ones with the so-called Radon-Nikodym property ([G-M2], [G-M4]).2)The embedding of separable reflexive Banach spaces into reflexive spaces with basis (fZl).3)The existence of long sequences of projections and hence of locally uniformly convex norms in the duals of Asplund spaces. ([F-G])

Dual spaces ofJB *-triples and the Radon-Nikodym property

1991 ◽  
Vol 208 (1) ◽  
pp. 327-334 ◽  
Author(s):  
L. J. Bunce ◽  
C. -H. Chu
Keyword(s):  
Dual Spaces ◽  
Nikodym Property

On the Radon-Nikodym Property in Jordan Triples

1987 ◽  
Vol 99 (3) ◽  
pp. 462 ◽  
Author(s):  
Cho-Ho Chu ◽  
Bruno Iochum
Keyword(s):  
Nikodym Property

scholarly journals Boundaries of Asplund spaces

2010 ◽  
Vol 259 (6) ◽  
pp. 1346-1368 ◽  
Author(s):  
B. Cascales ◽  
V.P. Fonf ◽  
J. Orihuela ◽  
S. Troyanski
Keyword(s):  
Asplund Spaces

Dunford-Pettis operators and the Radon-Nikodym property

1988 ◽  
Vol 50 (2) ◽  
pp. 183-188 ◽  
Author(s):  
V. Caselles
Keyword(s):  
Nikodym Property
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