On the range of n th order derivations acting on commutative Banach positive squares ℓ-algebras

Naoual Kouki; Mohamed Ali Toumi

Topological Algebra and its Applications (2015)

  • Volume: 3, Issue: 1, page 1-18
  • ISSN: 2299-3231

Abstract

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In this paper we prove that the image of a nth order derivation on real commutative Banach ℓ-algebras with positive squares is contained in the set of nilpotent elements.

How to cite

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Naoual Kouki, and Mohamed Ali Toumi. " On the range of n th order derivations acting on commutative Banach positive squares ℓ-algebras ." Topological Algebra and its Applications 3.1 (2015): 1-18. <http://eudml.org/doc/276427>.

@article{NaoualKouki2015,
abstract = {In this paper we prove that the image of a nth order derivation on real commutative Banach ℓ-algebras with positive squares is contained in the set of nilpotent elements.},
author = {Naoual Kouki, Mohamed Ali Toumi},
journal = {Topological Algebra and its Applications},
keywords = {f-algebra; almost f-algebra; Jacobson radical; nth order derivation; -algebra; locally one-dimensional space; universally complete; derivation},
language = {eng},
number = {1},
pages = {1-18},
title = { On the range of n th order derivations acting on commutative Banach positive squares ℓ-algebras },
url = {http://eudml.org/doc/276427},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Naoual Kouki
AU - Mohamed Ali Toumi
TI - On the range of n th order derivations acting on commutative Banach positive squares ℓ-algebras
JO - Topological Algebra and its Applications
PY - 2015
VL - 3
IS - 1
SP - 1
EP - 18
AB - In this paper we prove that the image of a nth order derivation on real commutative Banach ℓ-algebras with positive squares is contained in the set of nilpotent elements.
LA - eng
KW - f-algebra; almost f-algebra; Jacobson radical; nth order derivation; -algebra; locally one-dimensional space; universally complete; derivation
UR - http://eudml.org/doc/276427
ER -

References

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  13. [13] Singer. I. M and Wermer. J, Derivations on commutative normed algebras, Math. Ann. 129 (1955), 260-264. Zbl0067.35101
  14. [14] Thomas. M. P, The image of a derivation is contained in the radical, Ann. Math. (2) 128, No.3 (1988), 435-460. Zbl0681.47016
  15. [15] Toumi, M.A., Continuous generalized (ɵ,ɸ)-separating derivations on archimedean almost f -algebras, Asian-Eur. J. Math. 5 (3) (2012) 17. Paper No. 1250045. 
  16. [16] Toumi, A., Toumi, M.A., Order bounded derivations on Archimedean almost f -algebras, Positivity 14 (2) (2010) 239–245. [Crossref][WoS] Zbl1213.06014

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