On a Causal Linear Optimization Theorem

In this note we specialize our results on causal commutant lifting theory from Foias and Tannenbaum (J. Funct. Anal. 118 (1993), 407-441) and Foias et al. (Acta. Sci. Math. 57-(1993), 101-123) to operators with a certain structure which appear in control theory. For such operators, we give an elementary proof of the causal commutant lifting theorem.