Let $1\leqslant p. Denote $L(\ell_p)$ the space of bounded operators on $\ell_p$. Let $B_{L(\ell_q)}$ [was $B_{L(\ell_p)}$ ] be the closed unit ball of $L(\ell_q)$ [was $L(\ell_p)$] considered as a subset of $L(\ell_p)$ [was $L(\ell_p)$]. Is it closed in $L(\ell_p)$ [was $L(\ell_p)$]?
EDIT: I made a correction.
EDIT 2: You are right. Please delete my question.