On statistically köthe-toeplitz duals

Abstract

In the present paper, we introduce the concept of Δm-statistical boundedness of real (or complex) numbers sequences by using generalized difference operator Δm and examine relationships between Δm-statistical convergence, Δm-statistical Cauchiness and Δm-statistical boundedness. In addition to that we compute the Kothe-Toeplitz and generalized Kothe-Toeplitz duals of the set of all Δm-statistical bounded sequences. Moreover, we come up with the idea of statistical α and β duals of the sets of sequence which makes us capable of creating statistical equivalents of the notions of normality and perfectness of sequence spaces. © Element, Zagreb.