Limit Orders and Multilinear Forms on ${\ell }_p$ Spaces

Abstract

Since the concept of limit order is a useful tool to study operator ideals, we propose an analogous definition for ideals of multilinear forms. From the limit orders of some special ideals (of nuclear, integral, $r$-dominated and extendible multilinear forms) we derive some properties of them and show differences between the bilinear and $n$-linear cases ($n\ge 3$).