Nil, nilpotent and PI-algebras

Volume 30 / 1994

Vladimír Müller Banach Center Publications 30 (1994), 259-265 DOI: 10.4064/-30-1-259-265


The notions of nil, nilpotent or PI-rings (= rings satisfying a polynomial identity) play an important role in ring theory (see e.g. [8], [11], [20]). 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 [13], 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.


  • Vladimír Müller

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