Statistically multiplicative convergence on locally solid Riesz algebras - Aydin, Abdullah; ET, Mikail (Tubitak Scientific & Technological Research Council Turkey, 2021)
In this paper, we introduce the statistically multiplicative convergent sequences in locally solid Riesz algebras with respect to algebra multiplication and solid topology. We study this concept and the notion of st(m)-bounded sequences, and also, we prove some relations between this convergence and the other convergences such as the order convergence and the statistical convergence in topological spaces. Also, we give some results related to semiprime f-algebras.
Keywords: Statistically multiplicative convergence; statistically multiplicative bounded sequence; statistical convergence; Riesz algebra; Riesz spaces; locally solid Riesz spaces