Abstract
In 1936 Hamilton presented a Silverman-Toeplitz type characterization of c″0 (i.e. the space of bounded double Pringsheim null sequences). In this paper we begin with the presentation of a notion of asymptotically statistical regular. Using this definition and the concept of maximum remaining difference for double sequence, we present the following Silverman-Toeplitz type characterization of double statistical rate of convergence: let A be a nonnegative c″0−c″0 summability matrix and let [x] and [y] be member of l″ such that with [x] ∈ P0, and [y] ∈ Pδ for some δ > 0 then µ(Ax) µ(Ay). In addition other implications and variations shall also be presented.
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