# Definition:Left Shift Operator

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## Definition

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:

$\map L {x_1, x_2, x_3, \ldots} = \tuple {x_2, x_3, \ldots}$