I am very happy I got many comments for my first "technical" blog, where I made a question on relationship between zero and infinity norms in CS (compressed sensing).
Igor pointed out his blog entries (here and here) in his comment. According to the entry, an L-infinity optimization may produce a vector the elements of which are sticked to ±||x||_∞. Applying DFT to such a vector, e.g., x=(1,1,...,1), result in a sparse vector in the Fourier domain. This may be a simple explanation why the infinity norm is related to CS.
Mahesh and Thomas pointed out the infinity norm is also used in the Dantzig selector. This is based on the fact that L-1 (ell-1) is the dual vector space of L-infinity (ell-infinity). This is yet another link between zero and infinity (note that L-1 is related to L-0 by so many studies on CS). This also interests me very much.