On the Banach algebra (w_{\infty}(\Lambda),w_{\infty}(\Lambda)) and applications to the solvability of matrix equations in w_{\infty}(\Lambda)
Bruno de Malafosse, Eberhard Malkowsky · Publicationes Mathematicae Debrecen · 2014
We apply the characterisation of the class (w ∞ (Λ), w ∞ (Σ)) and the fact that this is a Banach algebra to study the solvability in w ∞ (Λ) of matrix equations of the form ∆ + ρ X = B and ∆ρX = B, where ∆ + ρ and ∆ρ are upper and lower triangular matrices.Finally, we obtain some results on infinite tridiagonal matrices considered as operators from w ∞ (Λ) into itself, and study the solvability in w ∞ (Λ) of matrix equations for tridiagonal matrices.