Operator Space Structures on $\ell^1(n).$
  We show that the complex normed linear space $\ell^1(n),$ $n>1,$ has no isometric embedding into $k\times k$ complex matrices for any $k\in \mathbb{N}$ and discuss a class of infinite dimensional operator space structures on it. 
Rajeev Gupta, Md Ramiz Reza
math.FA