For y ∈ ℝ, a sequence x = (x_n) ∈ ℓ^∞, and a non-negative regular matrix A, Bartoszewicz et. al., in 2015, defined the notion of the A-density δ_A(y) of the indices of those x_n that are close to y. Their main result states that if the set of limit points of (x_n) is countable and density δ_A(y) exists for any y ∈ ℝ where A is a non-negative regular matrix, then lim_n→∞(Ax)_n = ∑_y∈ℝδ_A(y) · y. In this note we first show that the result can be extended to a more general class of matrices and then consider a conjecture which naturally arises from our investigations.

Keywords: non-negative matrix, A-density, A-limit,ideal convergence, innite splice, conjecture (^*).