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Tytuł artykułu

On the range of nthorder derivations acting on commutative Banach positive squares ℓ-algebras

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Rocznik
Tom
3
Numer
1
Opis fizyczny
Daty
otrzymano
2014-01-13
zaakceptowano
2015-12-02
online
2015-12-31
Twórcy
autor
  • Département des Mathématiques, Faculté des Sciences de Bizerte, 7021,
    Zarzouna, Bizerte, Tunisie
  • Département des Mathématiques, Faculté des Sciences de Bizerte, 7021,
    Zarzouna, Bizerte, Tunisie
Bibliografia
  • [1] Ben Amor, F., On orthosymmetric bilinear maps, Positivity 14, No. 1, 123-134 (2010).[WoS]
  • [2] Beukers, F., Huijsmans, C.B., Pagter, B., Unital embedding and complexification of f -algebras,Math. Z., 183, 131-144, 1983.
  • [3] Boulabiar, K., Positive derivations on Archimedean almost f -rings, Order 19 (4) (2002) 385–395.[Crossref]
  • [4] Colville, P., Davis, G., Keimel, K., Positive derivations on f -rings, J. Aust. Math. Soc. A 23 (1977) 371–375.[Crossref]
  • [5] Ebanks, B and Ng, C.T, Homogeneous tri-additive forms and derivations, Linear Algebra Appl. 435, No. 11, 2731-2755 (2011).[WoS]
  • [6] Ebanks, B, Characterizing ring derivations of all orders via functional equations: results and open problems, Aequationesmathematicae, in press
  • [7] Henriksen, M., Smith, F.A., Some properties of positive derivations on f -rings, Contemp. Math. 8 (1982) 175–184.[Crossref]
  • [8] Johnson, B.E., Continuity of derivations on commutative algebras, Amer. J. Math. 91 (1969) 1–10
  • [9] Kouki, N., Toumi, M. A., Derivations on universally complete f -algebras, Indag. Math. 26 (1) (2015) 1-18.[Crossref]
  • [10] Nakai, Y., High order derivations I, Osaka Journal of Mathematics 7 (1970), 1-27.
  • [11] Osborn, H., Modules of differentials I, II, Math. Ann. 170 (1967), 221-244; 175 (1968), 146-158.
  • [12] Render, H., The radical of a Banach algebra with a closed cone, Rend. Del Cir. Mat. Palermo. Serie II (1989) 152-154.[Crossref]
  • [13] Singer. I. M and Wermer. J, Derivations on commutative normed algebras, Math. Ann. 129 (1955), 260-264.
  • [14] Thomas. M. P, The image of a derivation is contained in the radical, Ann. Math. (2) 128, No.3 (1988), 435-460.
  • [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] Toumi, A., Toumi, M.A., Order bounded derivations on Archimedean almost f -algebras, Positivity 14 (2) (2010) 239–245.[Crossref][WoS]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_taa-2015-0010
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