Lipschitz functions on classical spaces (Q1193550)

It is shown that if \(f\) is a Lipschitz function defined on the unit sphere of \(c_ 0\), then for every positive \(\varepsilon\) there is an infinite dimensional subspace of \(c_ 0\) on whose unit sphere \(f\) differs by less than \(\varepsilon\). The theorem is related to the open question if every space isomorphic to \(\ell_ p\) (for \(1<p<\infty\)) contains a subspace that is \((1+\varepsilon)\) isomorphic to \(\ell_ p\).