Silverman–Toeplitz theorem
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In mathematics the Silverman–Toeplitz theorem, first proved by Otto Toeplitz, is a result in summability theory characterizing matrix summability methods which are regular. A regular matrix summability method is a matrix transformation of a convergent sequence which preserves the limit.
[edit] Silverman–Toeplitz theorem
An infinite matrix 
with complex valued entries defines a regular summability method if and only if it satisfies all of the following properties
(any column sequences converge to 0)
(the sum of the rows converges to 1)
(the row sums are bounded)
[edit] References
- Toeplitz, O. (1911) "Über die lineare Mittelbildungen" Prace mat.-fiz., 22, 113-118 (the original paper in German)
