Statistically order compact operators on Riesz spaces

Abstract

In this paper, we state and establish the concept of compact operators defined between Riesz spaces with respect to statistical order convergence. An operator mapping any statistical order bounded sequence to a sequence with a statistical order convergent subsequence between Riesz spaces is called statistical order compact. Moreover, we also define the notion of statistical M-weakly compact operators. By applying these nontopological concepts, we obtain some new results about these operators.

Order Continuous Operators

“…While recent study extends the properties of unbounded order continuous operators from 𝒰𝒰 Riesz space into ℜ (Turan et al, 2022). Aydin and Gorokhova studied the concept of statistically continuous and bounded operators with statistically ordered convergent sequences on Riesz spaces (Aydin & Statistics, 2023). In this paper, some basic results from the theory of order continuous operators were studied with proofs as needed.…”