On matrix domains of triangles

We prove some general results for the determination of the β-duals of, and the characterisations of matrix transformations on matrix domains of arbitrary triangles in FK spaces. Our results contain almost all recently published ones as special cases. We also study the measure of noncompactness of several matrix transformations. In particular, we obtain some known results of Sember, give the corrected version of a recent result by Djolović, and study compact operators on some spaces of Altay, Başar and Mursaleen.