Definition:Left Shift Operator

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:

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

Also see

• Definition:Right Shift Operator
• Definition:Forward Shift Operator

Sources

• 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous) ... (next): Chapter $\S 2.1$: Continuous and linear maps. Linear transformations