Compact Operators on Spaces of Sequences of Weighted Means

Subject Analysis
Title Compact Operators on Spaces of Sequences of Weighted Means
Author(s) Eberhard Malkowsky and Faruk. Özger
Keywords Sequence spaces, matrix transformations, measure of noncompactness, compact operators
Abstract

We reduce the spaces a₀^{r}, a_{c}^{r}, a₀^{r}(Δ) and a_{c}^{r}(Δ) and simplify their dual spaces and the characterisations of matrix transformations on them in EmaFarAb.BIB.Mal2. We also obtain an estimate and a formula for the Hausdorff measure of noncompactness of some matrix operators on the spaces a₀^{r} and a_{c}^{r}, and the corresponding characterisations of compact matrix operators.