Norm estimates of product operators with application to domain decomposition

In this paper, we consider norm estimates for operators of the product form E=(I-T"j)...(I-T"1)(I-T"0) in an abstract Hilbert space. By imposing appropriate assumptions on T"j, explicit norm estimates for E are established. We then apply the abstract theory to convergence analysis of domain decomposition for nonsymmetric and indefinite second order elliptic problems.