In this paper, we discuss the domain of a recently defined conservative matrix, constructed by means of the Schröder numbers in the spaces of $p-$absolutely summable sequences and bounded sequences. We determine the $\beta-$duals of the Banach spaces, introduced here, and present characterization of some matrix operators. Moreover, we give the characterization of certain compact operators via the Hausdorff measure of noncompactness.
DAĞLI, MUHAMMET CİHAT
"Matrix mappings and compact operators for Schröder sequence spaces,"
Turkish Journal of Mathematics: Vol. 46:
6, Article 18.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss6/18