On the Ideal Convergence of Double Sequences in Locally Solid Riesz Spaces

Abstract

The aim of this paper is to define the notions of ideal convergence, $I$-bounded for double sequences in setting of locally solid Riesz spaces and study some results related to these notions. We also define the notion of $I^{*}$-convergence for double sequences in locally solid Riesz spaces and establish its relationship with ideal convergence.