On a generalized product of certain sequences
The author considers a generalized product of two sequences containing as a special case both the Cauchy product and the Dirichlet product of two sequences. In the main results (Theorems 1 and 2) he characterizes the closedness of that product in \(\ell_\infty (p)\) and \(c_0 (p)\), respectively, where \(p= (p_n)\) is a sequence of positive real numbers. The results in the special cases of the Cauchy product and the Dirichlet product due to \textit{I. J. Maddox} and \textit{M. A. L. Willey} [Indian J. Math. 16, 23-31 (1974; Zbl 0352.46007)] are discussed in Corollaries 1 through 4.
scientific article; zbMATH DE number 871082