 CARMA SEMINAR
 Speaker: Prof John Giles, School of Mathematical and Physical Sciences, The University of Newcastle
 Title: Persistence properties for Banach spaces
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 8^{th} Sep 2011
 Abstract:
We are interested in local geometrical properties of a Banach space which are preserved under natural embeddings in all even dual spaces. An example of this behaviour which we generalise is:
if the norm of the space $X$ is Fréchet differentiable at $x \in S(X)$ then the norm of the second dual $X^{**}$ is Fréchet differentiable at $\hat{x}\in S(X)$ and of $X^{****}$ at $\hat{\hat{x}} \in S(X^{****})$ and so on....
The results come from a study of Hausdorff upper semicontinuity properties of the duality mapping characterising general differentiability conditions satisfied by the norm.
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