The 2-summing norm of $lⁿ_p$ computed with <i>n</i> vectors

Abstract

The 2-summing norm of an n-dimensional Banach space computed with n vectors is known to belong between $n^1/2/√{2}$ and $n^1/2$. It is shown that the 2-summing norm of real $l₁³$ computed with three vectors is 5/3. Some lower estimates for 2-summing norms of $l_pⁿ$ computed with n vectors are stated, which are considerably better than universal ones and are based on the existence of certain block designs or Hadamard matrices.