# Nil, nilpotent and PI-algebras

Banach Center Publications (1994)

- Volume: 30, Issue: 1, page 259-265
- ISSN: 0137-6934

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topMüller, Vladimír. "Nil, nilpotent and PI-algebras." Banach Center Publications 30.1 (1994): 259-265. <http://eudml.org/doc/262845>.

@article{Müller1994,

abstract = {
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.
},

author = {Müller, Vladimír},

journal = {Banach Center Publications},

keywords = {polynomial identity; Gelfand theory of Banach PI-algebras; Banach nil, nilpotent and PI-algebras},

language = {eng},

number = {1},

pages = {259-265},

title = {Nil, nilpotent and PI-algebras},

url = {http://eudml.org/doc/262845},

volume = {30},

year = {1994},

}

TY - JOUR

AU - Müller, Vladimír

TI - Nil, nilpotent and PI-algebras

JO - Banach Center Publications

PY - 1994

VL - 30

IS - 1

SP - 259

EP - 265

AB -
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.

LA - eng

KW - polynomial identity; Gelfand theory of Banach PI-algebras; Banach nil, nilpotent and PI-algebras

UR - http://eudml.org/doc/262845

ER -

## References

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- [18] Y. P. Razmyslov, Trace identities of full matrix algebras over a field of characteristic zero, Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 723-756 (in Russian).
- [19] G. C. Rota and W. G. Strang, A note on the joint spectral radius, Indag. Math. 22 (1960), 379-381. Zbl0095.09701
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- [22] Yu. V. Turovskiĭ, Spectral properties of certain Lie subalgebras and the spectral radius of subsets of a Banach algebra, in: Spectral Theory of Operators and its Applications, No. 6, Elm, Baku, 1985, 144-181 (in Russian).

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