Banach lattice

Summary

A Banach lattice is a Banach space with an order that is compatible with the vector operations and with the norm. Every two elements have a largest lower bound and a least upper bound, and a smaller absolute value gives a smaller norm. The spaces $L^p$, $C(K)$ and $\ell^p$ with the pointwise order are the main examples. Banach lattices are the setting for positive operators, which appear in probability, in partial differential equations and in economics.