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, Tome 3 (2015), / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:276427 
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     author = {Naoual Kouki and Mohamed Ali Toumi},
     title = {
      On the range of n
      th
      order derivations acting on commutative Banach positive squares l-algebras
    },
     journal = {Topological Algebra and its Applications},
     volume = {3},
     year = {2015},
     zbl = {1319.46037},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_taa-2015-0010}
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Naoual Kouki; Mohamed Ali Toumi. 
      On the range of n
      th
      order derivations acting on commutative Banach positive squares ℓ-algebras
    . Topological Algebra and its Applications, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_taa-2015-0010/

[1] Ben Amor, F., On orthosymmetric bilinear maps, Positivity 14, No. 1, 123-134 (2010). [WoS] | Zbl 1204.06010

[2] Beukers, F., Huijsmans, C.B., Pagter, B., Unital embedding and complexification of f -algebras,Math. Z., 183, 131-144, 1983. | Zbl 0494.06010

[3] Boulabiar, K., Positive derivations on Archimedean almost f -rings, Order 19 (4) (2002) 385–395. [Crossref] | Zbl 1025.06015

[4] Colville, P., Davis, G., Keimel, K., Positive derivations on f -rings, J. Aust. Math. Soc. A 23 (1977) 371–375. [Crossref] | Zbl 0376.06021

[5] Ebanks, B and Ng, C.T, Homogeneous tri-additive forms and derivations, Linear Algebra Appl. 435, No. 11, 2731-2755 (2011). [WoS] | Zbl 1230.39011

[6] Ebanks, B, Characterizing ring derivations of all orders via functional equations: results and open problems, Aequationes mathematicae, in press

[7] Henriksen, M., Smith, F.A., Some properties of positive derivations on f -rings, Contemp. Math. 8 (1982) 175–184. [Crossref] | Zbl 0491.06016

[8] Johnson, B.E., Continuity of derivations on commutative algebras, Amer. J. Math. 91 (1969) 1–10 | Zbl 0181.41103

[9] Kouki, N., Toumi, M. A., Derivations on universally complete f -algebras, Indag. Math. 26 (1) (2015) 1-18. [Crossref] | Zbl 1319.46037

[10] Nakai, Y., High order derivations I, Osaka Journal of Mathematics 7 (1970), 1-27. | Zbl 0197.31501

[11] Osborn, H., Modules of differentials I, II, Math. Ann. 170 (1967), 221-244; 175 (1968), 146-158. | Zbl 0154.03704

[12] Render, H., The radical of a Banach algebra with a closed cone, Rend. Del Cir. Mat. Palermo. Serie II (1989) 152-154. [Crossref] | Zbl 0698.46041

[13] Singer. I. M and Wermer. J, Derivations on commutative normed algebras, Math. Ann. 129 (1955), 260-264. | Zbl 0067.35101

[14] Thomas. M. P, The image of a derivation is contained in the radical, Ann. Math. (2) 128, No.3 (1988), 435-460. | Zbl 0681.47016

[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] | Zbl 1213.06014