An index theorem for the product of linear relations Original Research Article

Let X, Y and Z be vector spaces and let T and S be linear relations from X to Y and Y to Z, respectively, with S everywhere defined on Y. A formula which relates the nullities and deficiencies of S, T and ST is derived. In the case when S and T have finite indices (in particular, when the vector spaces are all finite dimensional), then ST has an index given by imageindex(ST)=index(S)+index(T)−dimT(0)∩S−1(0) The familiar index formula for the product of Fredholm operators is covered by the case T(0) = {0}.