An article co-authored by Professor of Mathematics Robert Kantrowitz ’82 appears in the 2016 volume of the International Journal of Mathematics and Mathematical Sciences. “More of Dedekind: His Series Test in Normed Spaces” was written with Michael M. Neumann of Mississippi State University.
The classical version of Dedekind’s test from real analysis determines convergence for certain infinite series of real numbers. In their paper, Kantrowitz and Neumann discuss the fate of Dedekind’s infinite series test in the context of normed linear spaces and normed algebras.
The main result is that a normed space is sequentially or Cauchy complete precisely when Dedekind’s series test holds. Dedekind’s test thus joins the absolute convergence test in its ability to characterize those normed linear spaces that are Banach spaces.
