Generalized difference spaces of non-absolute type of convergent and null sequences
Summary: The aim of the present paper is to introduce the spaces \(c^\lambda_0(B)\) and \(c^\lambda(B)\) of generalized difference sequences. These spaces are \(BK\)-spaces of non-absolute type and norm isomorphic to the spaces \(c_0\) and \(c\), respectively. Furthermore, we derive some inclusion relations, determine the \(\alpha\)-, \(\beta\)-, and \(\gamma\)-duals of those spaces, and construct their Schauder bases. Finally, we characterize some matrix classes from the spaces \(c^\lambda_0(B)\), and \(c^\lambda(B)\) to the spaces \(\ell_p\), \(c_0\), and \(c\).
scientific article; zbMATH DE number 6134090
scientific article