The Baire classification of strongly separately continuous functions on ${\ell }_{\infty }$

Abstract

We prove that for any $\alpha \in [0,{\omega }_1)$ there exists a strongly separately continuous function $f:{\ell }_{\infty }\to [0,1]$ such that $f$ belongs to the $(\alpha +1)$'th /$(\alpha +2)$'th/ Baire class and does not belong to the $\alpha$'th Baire class if $\alpha$ is finite /infinite/.