Abstract
Tuǧ and Basar [3] have recently studied the concept of four dimensional generalized difference matrix B(r, s, t, u) and its matrix domain in some double sequence spaces. In this present paper, as a natural continuation of [3], we introduce new almost null and almost convergent double sequence spaces \(B(C_f)\) and \(B(C_{f_0})\) as the domain of four-dimensional generalized difference matrix B(r, s, t, u) in the spaces \(C_f\) and \(C_{f_0}\), respectively. Firstly, we prove that the spaces \(B(C_f)\) and \(B(C_{f_0})\) of double sequences are Banach spaces under some certain conditions. We give some inclusion relations with some topological properties. Moreover, we determine the \(\alpha -\) dual , \(\beta (bp)-\)dual and \(\gamma -\) dual of the spaces \(B(C_f)\). Finally, we characterize the classes of four dimensional matrix mappings defined on the spaces \(B(C_f)\) of double sequences.
Published Version
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