I see that Wold's theorem in time series analysis is proven by the abstract Wold's decomposition in operator theory. The abstract theorem states that:
Every isometry is a direct sum of copies of the unilateral shift and a unitary operator.
I want to understand intuitively the connection between the two theorems: so in the time series version $Y_t = \sum_{j=0}^\infty b_j \epsilon_{t-j} + \eta_t$, which are the isometry, the shift and the unitary operator?
PS: I see in some document which states the lag operator is the isometry, then which is the shift operator in the time series version?