(V, Λ)-Order SUMMABLE IN RIESZ SPACES

Abstract

Statistical convergence is an active area, and it appears in a wide variety of topics. However, it has not been studied extensively in Riesz spaces. There are a few studies about the statistical convergence on Riesz spaces, but they only focus on the relationship between statistical and order convergences of sequences in Riesz spaces. In this paper, we introduce the notion of (V, λ)-order summable by using the concept of λ- statistical monotone and the λ-statistical order convergent sequences in Riesz spaces. Moreover, we give some relations between (V, λ)-order summable and λ-statistical order convergence.

StatisticalLY τ-Bounded Operators on Ordered Topological Vector Spaces

“…A vector lattice introduced by Riesz in [1] is an ordered vector space, and it has many applications in measure theory, operator theory, and applications in economics [2][3][4]. On the other hand, the statistical convergence is a generalization of the ordinary convergence of a real sequence [5][6][7][8]. One study related to this paper is done by Troitsky [9] where the bb-and nb-bounded operators were defined between topological vector spaces and another one is done by Aydın [10] in which the ob-bounded operator was defined from vector lattices to locally solid vector lattice.…”