Some degenerate binomial sequence spaces and related matrix transformations and compactness

The main goal of this paper is to introduce some degenerate binomial sequence spaces and to mention that these are linearly isomorphic to the spaces \(c_{0}\) $c_0$ and c. As well, we establish \(\alpha\) $\alpha$ -, \(\beta\) $\beta$ -, \(\gamma\) $\gamma$ -duals for these spaces and certain characterizations for some matrix classes. As an application, we deduce the characterization of certain compact operators via the Hausdorff measure of noncompactness.