Almost sequence spaces derived by the domain of the matrix \(A^r\) (Q2319104)

Summary: By using \(A^r\), we introduce the sequence spaces \(a_f^r\), \(a_{f_0}^r\), and \(a_{fs}^r\) of normed space and \(BK\)-space and prove that \(a_f^r\), \(a_{f_0}^r\), and \(a_{fs}^r\) are linearly isomorphic to the sequence spaces \(f\), \(f_0\), and \(fs\), respectively. Further, we give some inclusion relations concerning the spaces \(a_f^r\), \(a_{f_0}^r\), and the nonexistence of Schauder basis of the spaces \(fs\) and \(a_{fs}^r\) is shown. Finally, we determine the \(\beta\)- and \(\gamma\)-duals of the spaces \(a_f^r\) and \(a_{fs}^r\). Furthermore, the characterization of certain matrix classes on new almost convergent sequence and series spaces has exhaustively been examined.