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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 ]
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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. Here is how Gottfried Köthe, who was Toeplitz's assistant in Bonn, described their collaboration: Otto liked to take walks and talk about scientific questions. I in fact needed a piece of paper and pencil to write everything down. Toeplitz convinced me that the great outline of research comes to light best in dialog.
In mathematical analysis, the Szegő limit theorems describe the asymptotic behaviour of the determinants of large Toeplitz matrices. [ 1 ] [ 2 ] [ 3 ] They were first proved by Gábor Szegő . Notation
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).
Theorem (Coburn) C*(V) is isomorphic to the Toeplitz algebra and V is the isomorphic image of T z. The proof hinges on the connections with C(T), in the description of the Toeplitz algebra and that the spectrum of a unitary operator is contained in the circle T. The following properties of the Toeplitz algebra will be needed: