On band operators

Let G and H be Archimedean Riesz spaces. We study the properties of band operators and inverse band operators from G to H and investigate their relations to some well-known classes of operators. Then, we show that under some assumptions on the Riesz spaces G or H, if S is a bijective band operator from G into H then S-1 : H -> G is a band operator. Additionally, we give some conditions under which a band operator becomes order bounded