Orthogonal Projection and Restricted Subordination of Hubert-Schmidt Operator-Valued Stationary Processes

Abstract

The paper contains two results on subordination of stationarily correlated Hilbert-Schmidt operator-valued stationary processes. First an explicit form of the spectral measure of the orthogonal projection of one process onto another is stated. On the basis of this result B. Fritzsche’s and B. Kirstein’s solution of the restricted subordination problem for finite-dimensional processes is generalized to Hilbert-Schmidt operator-valued processes.