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In mathematics, the Silverman–Toeplitz theorem, first proved by Otto Toeplitz, is a result in series summability theory characterizing matrix summability methods that are regular. A regular matrix summability method is a linear sequence transformation that preserves the limits of convergent sequences . [ 1 ]
Toeplitz algebra, the C*-algebra generated by the unilateral shift on the Hilbert space; Toeplitz Hash Algorithm, used in many network interface controllers; Hellinger–Toeplitz theorem, an everywhere defined symmetric operator on a Hilbert space is bounded; Silverman–Toeplitz theorem, characterizing matrix summability methods which are regular
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Otto Toeplitz and Alexander Ostrowski. Toeplitz was born to a Jewish family of mathematicians. Both his father and grandfather were Gymnasium mathematics teachers and published papers in mathematics. Toeplitz grew up in Breslau and graduated from the Gymnasium there.
Louis Lazarus Silverman (21 April 1884 – 17 October 1967) was an American mathematician, the first person to receive a Ph.D. in mathematics from an academic institution in the state of Missouri. [1] [2] Born in a village in Lithuania, Silverman moved with his parents to the United States when he was eight years old.
Let () = be a sequence, and let = + + = = be its k th partial sum.. The sequence (a n) is called Cesàro summable, with Cesàro sum A ∈ , if, as n tends to infinity, the arithmetic mean of its first n partial sums s 1, s 2, ..., s n tends to A:
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An Toeplitz matrix may be defined as a matrix where , =, for constants , …,.The set of Toeplitz matrices is a subspace of the vector space of matrices (under matrix addition and scalar multiplication).