Definition:Infinite Limit Operator

Definition

Let $c$ be the space of convergent sequences.

Let $\mathbf x := \sequence {x_n}_{n \mathop \in \N} \in c$.

Let $\R$ be the set of real numbers.

The infinite limit operator, denoted by $L$, is the mapping $L : c \to \R$ such that:

$\ds \map L {\mathbf x} := \lim_{n \mathop \to \infty} x_n$

Also see

• Definition:Limit of Sequence

Sources

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