Asymptotic Isometries for Lacunary Muntz Spaces and Applications

摘要

We prove that the normalized sequence ((pn+1)1/ptn))nZ in Lp([0,1]), up to some truncation, is asymptotically isometric to the canonical basis of p if and only if it is almost isometric if and only if (n+1/p)n (resp. (n)n) is a super-lacunary sequence. This extends recent results of the same authors. Similar results occur in C([0,1]). As a particular application, we get that all the (strict) s-numbers of the classical Cesaro operator on Lp are equal to p when p is an element of(1,+ infinity).