FUNCTIONS PRESERVING SEQUENCE SPACES
Grinnell · Real Analysis Exchange · 1998
Let A and B be sets of real sequences.Let F (A, B) denote the set of functions f : R → R that preserve A and B in the sense that (f (an)) ∈ B for all sequences (an) ∈ A. These functions are generalizations of convergence preserving functions first introduced by Rado.We establish identities and inclusions for F (A, B) when A and B are l p -spaces and other well-known sequence spaces.We also characterize F (A, B) in terms of elementary classes of functions.Our characterizations are motivated by the work of Borsík, Červeňanský and Šalát.