Compactness of matrix operators on some new difference sequence spaces (Q648917)

The authors establish some identities or estimates for the Hausdorff measures of noncompactness of certain matrix operators on the difference sequence spaces \[ c_{o}^{\lambda }(\Delta) = \Big\{ ( x_{k}):\;\lim_{n\rightarrow \infty }\frac{1}{\lambda _{n}}\sum_{k=0}^{n} ( \lambda _{k}-\lambda _{k-1})(x_{k}-x_{k-1}) =0\Big\} \] and \[ \ell_\infty^{\lambda }( \Delta) = \Big\{( x_{k}): \sup_{n}\left|\frac{1}{\lambda _{n}}\sum_{k=0}^{n}(\lambda _{k}-\lambda _{k-1})(x_{k}-x_{k-1})\right|<+\infty\Big\}\,, \] where \(\lambda =\left( \lambda _{k}\right)\) is a strictly increasing sequence of positive real numbers tending to infinity; see [\textit{M. Mursaleen} and \textit{A. K. Noman}, Math. Comput. Modelling 52, No.~ 3--4, 603--617 (2010; Zbl 1201.40003)]. Furthermore, they characterize some classes of compact operators on these spaces.