nonreflexive space
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A generalization of a renorming theorem by Lin and a new nonreflexive space with the fixed point property which is nonisomorphic tol1

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2013.03.062 ◽

2013 ◽

Vol 405 (1) ◽

pp. 57-70 ◽

Cited By ~ 2

Author(s):

Berta Gamboa de Buen ◽

Fernando Núñez-Medina

Keyword(s):

Fixed Point ◽

Fixed Point Property ◽

Point Property ◽

Nonreflexive Space

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In a nonreflexive space the subdifferential is not onto

Mathematische Zeitschrift ◽

10.1007/bf01168159 ◽

1985 ◽

Vol 189 (4) ◽

pp. 555-560 ◽

Cited By ~ 2

Author(s):

Simon Fitzpatrick ◽

Bruce Calvert

Keyword(s):

Nonreflexive Space

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A Non-Reflexive Smooth Space with a Smooth Dual

Canadian Mathematical Bulletin ◽

10.4153/cmb-1974-103-4 ◽

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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