arXiv subjects
Publications and source records attributed to N. Tenney Peck.
We prove that if PT is a factorization of the identity operator on \ell_p^n through \ell_{\infty}^k, then ||P|| ||T|| \geq Cn^{1/p-1/2}(log n)^{-1/2}. This is a corollary of a more general result on factoring the identity operator on a quasi-normed space through \ell_{\infty}^k.
Let F be a quasi-linear map on a separable normed space X, and assume that F splits on an infinite-dimensional subspace of X. Then the twisted sum topology induced by F on the direct sum of X and the real line can be written as the supremum of a nearly convex topology and a trivial dual topology. (This partially answers a question of Klee.) The result applies when X is \ell_1 and F is the Ribe function or when X is James's space.