ON STATISTICALLY KOTHE-TOEPLITZ DUALS - Temizsu, Fatih; Et, Mikail (Element, 2019)
In the present paper, we introduce the concept of Delta(m)-statistical boundedness of real (or complex) numbers sequences by using generalized difference operator Delta(m) and examine relationships between Delta(m)-statistical convergence, Delta(m)-statistical Cauchiness and Delta(m) -statistical boundedness. In addition to that we compute the Kothe-Toeplitz and generalized Kothe-Toeplitz duals of the set of all Delta(m)- statistical bounded sequences. Moreover, we come up with the idea of statistical alpha and beta duals of the sets of sequence which makes us capable of creating statistical equivalents of the notions of normality and perfectness of sequence spaces.
Keywords: Statistical boundedness; dual spaces