Archive for February 17th, 2009

Must an “explicitly defined” Banach space contain c_0 or ell_p?

February 17, 2009

I do not know how to make this question fully precise (except in ways that make the answer uninteresting), but I have wondered about it for a long time, and it has arisen again in the discussion following my recent post on the Banach space constructed by Spiros Argyros and Richard Haydon. Here I would like to say enough to enable others to think about it. One could think of this post as the beginning of polymath2, but I expect polymath2 to be somewhat different from polymath1 for various reasons: it will involve different people, it may well go much more slowly than polymath1 (I would like to think of it quietly chugging away in the background), and I am not comfortable with some of the mathematics that will be essential to formulating a good conjecture. On a more practical level, I think that having a wiki for polymath 1 (see my blogroll for a link) has worked very well as a way of organizing our collective thoughts on the density Hales-Jewett theorem, and if polymath2 gets off the ground then I would expect an accompanying wiki to be part of it from the very beginning. (more…)