Silverman–Toeplitz theorem

In mathematics, the Silverman–Toeplitz theorem, first proved by Otto Toeplitz, is a result in summability theory characterizing matrix summability methods that are regular. A regular matrix summability method is a matrix transformation of a convergent sequence which preserves the limit.

An infinite matrix ${\displaystyle (a_{i,j})_{i,j\in \mathbb {N} }}$ with complex-valued entries defines a regular summability method if and only if it satisfies all of the following properties:

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