Nil, nilpotent and PI-algebras
The notions of nil, nilpotent or PI-rings (= rings satisfying a polynomial identity) play an important role in ring theory (see e.g. , , ). Banach algebras with these properties have been studied considerably less and the existing results are scattered in the literature. The only exception is the work of Krupnik , where the Gelfand theory of Banach PI-algebras is presented. However, even this work has not get so much attention as it deserves. The present paper is an attempt to give a survey of results concerning Banach nil, nilpotent and PI-algebras. The author would like to thank to J. Zemánek for essential completion of the bibliography.