Summary: We establish some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on the spaces

${c}_{0}^{\lambda}$ and

${\ell}_{\infty}^{\lambda}$which have recently been introduced in [

*M. Mursaleen* and

*A. K. Noman*, “On the spaces of

$\lambda $-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.