$\lambda$-Convergence and $\lambda$-Conullity

Abstract

The notions of $\lambda$-convergence and $\lambda$-summabihty was first defined a couple of decades ago by C. Kangro and has been further studied by Kangro and his school at Tartu University. In analogy to the usual notions of coregularity and conullity of conservative (matrix-) methods, he has introduced, inter alia, $\lambda$-coregularity and $\lambda$-conullity for $\lambda$-conservative matrices. Here we compare $\lambda$-conullity with the general notion of conullity of an $FK$-space with respect to a subspace which was introduced in [2]. To this end we show that the space $c^{\lambda }$ of all $\lambda$-convergent sequences is of type $c_D$, a summability domain. As a consequence, we prove that the space of all sequences that are $\lambda$-summable by a given matrix $A$ is a summability domain $c_E$ for some matrix $E$.