  For an open set $\Om \subset \R^2$ let $\lambda(\Om)$ denote the bottom of
the spectrum of the Dirichlet Laplacian acting in $L^2(\Om)$. Let $w_\Om$ be
the torsion function for $\Om$, and let $\|.\|_p$ denote the $L^p$ norm. It is
shown there exists $\eta>0$ such that $\|w_{\Om}\|_{\infty} \lambda(\Om)\ge
1+\eta$ for any non-empty, open, simply connected set $\Om\subset \R^2$ with
$\lb(\Om) >0$. Moreover, if the measure $|\Om|$ of $\Om$ is finite, then
$\|w_{\Om}\|_1\lambda(\Om)\le (1-\eta)|\Om|$.
