Summary: We establish some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on the spaces
which have recently been introduced in [M. Mursaleen
and A. K. Noman
, “On the spaces of
-convergent and bounded sequences”, Thai J. Math. 8, No. 2, 311–329 (2010; Zbl 1218.46005
)]. Further, by using the Hausdorff measure of noncompactness, we characterize some classes of compact operators on these spaces.