On band operators

Abstract

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