On some sequence spaces defined by a modulus
There are ten results in this paper. The following result typifies the standard of the results: For any nonnegative regular matrix \(A= (a_{nk})\) and moduli \(f\) and \(g\), \[ w_\infty(A, g)\subset w_\infty(A, f)\Leftrightarrow \limsup_{x\to\infty} {f(x)\over g(x)}< \infty, \] where \[ w_\infty(A, f)= \Biggl\{(x_k): \sup_n \sum^\infty_{k=1} a_{nk} f(|x_k|)< \infty\Biggr\}. \] Information on multipliers for \(w_\infty(A, f)\) is also given. There is a result on conditions under which \(w_\infty(A,f)= s\), the space of all complex sequences.
scientific article; zbMATH DE number 1359898