Some Properties of Causal Linear Time-Invariant(LTI) Operators on the Weighted ?_2 Space

We discuss the properties of causal LTI operators on weighted ?2 spaces for different choices of the weighting sequence {w(t)}t∈Z. Problems of closability of unstable causal LTI convolution operators are also discussed. We shall provide a new type of argument concerning causal LTI operators and robust design that can be applied to a large class of weighted ?2 spaces on Z.