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 ${\lambda }_{cb}(E)=\sqrt{n}$ if and only if $ex(E)=\sqrt{n}$, which is equivalent to ${\lambda }_{cb}(E)<\sqrt{n}$ if and only if $ex(E)<\sqrt{n}$.

7 pages, The whole paper is reorganized