Matrix valued versions of a result of von Neumann with an application to time discretization

摘要

We study the size of the operator C(A) where C(z) is an n×m-matrix with rational elements such that |C(z)|⩽1 in some norm for all complex z in the unit disc, and A is a linear operator in a Hilbert space with norm at most 1. An application to variable step integration of initial value problems using one-leg methods is given.