  We study strongly separately continuous real-valued function defined on the
Banach spaces $\ell_p$. Determining sets for the class of strongly separately
continuous functions on $\ell_p$ are characterized. We prove that for every
$1\le \alpha<\omega_1$ there exists a strongly separately continuous function
which belongs the $(\alpha+1)$'th Baire class and does not belong to the
$\alpha$'th Baire class on $\ell_p$. We show that any open set in $\ell_p$ is
the set of discontinuities of a strongly separately continuous real-valued
function.
