This is an announcement for the paper "Hadamard differentiability via Gateaux differentiability" by Ludek Zajicek.

Abstract: Let $X$ be a separable Banach space, $Y$ a Banach space and $f: X \to Y$ a mapping. We prove that there exists a $\sigma$-directionally porous set $A\subset X$ such that if $x\in X \setminus A$, $f$ is Lipschitz at $x$, and $f$ is G^ateaux differentiable at $x$, then $f$ is Hadamard differentiable at $x$. If $f$ is Borel measurable (or has the Baire property) and is G^ ateaux differentiable at all points, then $f$ is Hadamard differentiable at all points except a set which is $\sigma$-directionally porous set (and so is Aronszajn null, Haar null and $\Gamma$-null). Consequently, an everywhere G^ ateaux differentiable $f: \R^n \to Y$ is Fr' echet differentiable except a nowhere dense $\sigma$-porous set.

Archive classification: math.FA

Mathematics Subject Classification: Primary: 46G05, Secondary: 26B05, 49J50

Remarks: 9 pages

Submitted from: zajicek@karlin.mff.cuni.cz

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1210.4715

or

http://arXiv.org/abs/1210.4715