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DUAL DIFFERENTIATION SPACES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 99 / Issue 3 / June 2019
- Published online by Cambridge University Press:
- 28 March 2019, pp. 467-472
- Print publication:
- June 2019
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- Article
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- You have access
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We show that if
$(X,\Vert \cdot \Vert )$ is a Banach space that admits an equivalent locally uniformly rotund norm and the set of all norm-attaining functionals is residual then the dual norm 
$\Vert \cdot \Vert ^{\ast }$ on 
$X^{\ast }$ is Fréchet at the points of a dense subset of 
$X^{\ast }$. This answers the main open problem in a paper by Guirao, Montesinos and Zizler [‘Remarks on the set of norm-attaining functionals and differentiability’, Studia Math.241 (2018), 71–86].
