Extremal cases of exactness constant and completely bounded projection constant

Abstract

We investigate some extremal cases of exactness constant and completely bounded projection constant. More precisely, for an $n$-dimensional operator space $E$ we prove that $λ_{cb}(E) = \sqrt{n}$ if and only if $ex(E) = \sqrt{n}$, which is equivalent to $λ_{cb}(E) < \sqrt{n}$ if and only if $ex(E) < \sqrt{n}$.