Paper detail

On strongly separately continuous functions on sequence spaces

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 $1\le α<ω_1$ there exists a strongly separately continuous function which belongs the $(α+1)$'th Baire class and does not belong to the $α$'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.