Definition:Cesàro Summation Operator
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Definition
Let $\ell^\infty$ be the space of bounded sequences.
Let $\sequence {x_n}_{n \mathop \in \N} \in \ell^\infty$ be a sequence.
Let $A : \ell^\infty \to \ell^\infty$ be an operator such that:
- $\ds \map A {x_1, x_2, x_3, \ldots} = \tuple {x_1, \frac {x_1 + x_2} 2, \frac {x_1 + x_2 + x_3} 3, \ldots}$
Then $A$ is called the Cesàro summation operator.
Also known as
The Cesàro summation operator is also known as the averaging operator.
Also see
- Results about the Cesàro summation operator can be found here.
Source of Name
This entry was named for Ernesto Cesàro.
Sources
- 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous) ... (next): Chapter $\S 2.3$: The normed space $\map {CL} {X,Y}$. Operator norm and the normed space $\map {CL} {X, Y}$