\begin{definition}[Definition:Left Shift Operator]
Let $X, Y$ be sequence spaces.
Let $x := \tuple {x_1, x_2, x_3, \ldots} \in X$.
The '''left shift operator''', denoted by $L$, is the mapping $L : X \to Y$ such that:
:$\map L {x_1, x_2, x_3, \ldots} = \tuple {x_2, x_3, \ldots}$
\end{definition}