In this paper a linear time-invariant, discrete-time system is considered by regarding it as an (unbounded) operator on l(2)(N), l(2)(Z), C-N or C-Z. The graphs of closed systems ar characterized and properties such as causality and closability of systems are studied. It si shown that the closure of a causal, closable system on l(2)(N), C-N and C-Z is again causal, whereas this is in general not the case for systems on l(2)(Z). Necessary and sufficient condition which guarantee that this property hold for systems on l(2)(Z) are given. Many of the results extend without change to the continuous-time case.