Let and be two vector spaces over the same ordered field (for example; ), and they are equipped with norms. Then a linear operator from to is called bounded if there exists such that for every '''' in . Bounded operators form a vector space. On this vector space we can introduce a norm that is compatible with the norms of and : In case of operators from to itself it can be shown that .
let and be two vector spaces over the same ordered field (for example; ) and they are equipped with norms then a linear operator from to is called bounded if there exists such that for every '''' in  bounded operators form a vector space on this vector space we can introduce a norm that is compatible with the norms of and  in case of operators from to itself it can be shown that 