“Banach algebras of sequences of generalized bounded variation,” co-authored by Robert Kantrowitz ’82, the Marjorie and Robert W. McEwen Professor of Mathematics, and John A. Lindberg, Jr., late professor emeritus of Syracuse University, was recently published in the research journal Archiv der Mathematik.
The study of abstract Banach algebras – named for the 20th century Polish mathematician, Stefan Banach – took hold in the 1940s as a sub-branch of the mathematical area of functional analysis, Kantrowitz said.
In their paper, he and Lindberg shed light on various properties of the class of Banach algebras of sequences of generalized bounded variation. In particular, the authors show that the carrier spaces of such algebras are homeomorphic to compactifications of the discrete space of positive integers.
They provide necessary and sufficient conditions under which the carrier space may be identified with the one-point compactification or the Stone–Cech compactification of the positive integers, and also that the carrier spaces of many of the Banach algebras under consideration are neither of these familiar compactifications.
Posted September 19, 2025
