On strongly separately continuous functions on sequence spaces

Abstract

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.