“A unifying view of some Banach algebras,” by Robert Kantrowitz ’82, the Marjorie and Robert W. McEwen Professor of Mathematics, was recently published in The Australian Journal of Mathematical Analysis and Applications (volume 20, 2023).
Kantrowitz says the study of abstract Banach algebras, named for 20th century Polish mathematician Stefan Banach, took hold in the 1940s as a sub-branch of the mathematical area of functional analysis.
In his article, Kantrowitz provides an alternative lens through which to view a host of normed algebras and offers a unifying framework that encompasses many familiar Banach algebras. In addition, recognition that a normed linear space conforms to this general structure provides another avenue to confirming that it is at once stable under multiplication and also outfitted with an abundance of equivalent submultiplicative norms.
