In a nonreflexive space the subdifferential is not onto

1985 ◽  
Vol 189 (4) ◽  
pp. 555-560 ◽  
Author(s):  
Simon Fitzpatrick ◽  
Bruce Calvert
Keyword(s):  
Nonreflexive Space

A Non-Reflexive Smooth Space with a Smooth Dual

1974 ◽  
Vol 17 (4) ◽  
pp. 579-580
Author(s):  
J. H. M. Whitfield
Keyword(s):  
Banach Space ◽  
Real Banach Space ◽  
Gâteaux Differentiability ◽  
Fréchet Differentiability ◽  
Smooth Norm ◽  
Frechet Differentiability ◽  
Gateaux Differentiability ◽  
Fréchet Differentiable ◽  
Smooth Space ◽  
Nonreflexive Space

Let (E, ρ) and (E*ρ*) be a real Banach space and its dual. Restrepo has shown in [4] that, if p and ρ* are both Fréchet differentiable, E is reflexive. The purpose of this note is to show that Fréchet differentiability cannot be replaced by Gateaux differentiability. This answers negatively a question raised by Wulbert [5]. In particular, we will renorm a certain nonreflexive space with a smooth norm whose dual is also smooth.

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