Applying the density theorem for derivations to range inclusion problems
Studia Mathematica (2000)
- Volume: 138, Issue: 1, page 93-100
- ISSN: 0039-3223
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topBeidar, K., and Brešar, Matej. "Applying the density theorem for derivations to range inclusion problems." Studia Mathematica 138.1 (2000): 93-100. <http://eudml.org/doc/216692>.
@article{Beidar2000,
abstract = {The problem of when derivations (and their powers) have the range in the Jacobson radical is considered. The proofs are based on the density theorem for derivations.},
author = {Beidar, K., Brešar, Matej},
journal = {Studia Mathematica},
keywords = {derivations; Jacobson radical; Banach algebras},
language = {eng},
number = {1},
pages = {93-100},
title = {Applying the density theorem for derivations to range inclusion problems},
url = {http://eudml.org/doc/216692},
volume = {138},
year = {2000},
}
TY - JOUR
AU - Beidar, K.
AU - Brešar, Matej
TI - Applying the density theorem for derivations to range inclusion problems
JO - Studia Mathematica
PY - 2000
VL - 138
IS - 1
SP - 93
EP - 100
AB - The problem of when derivations (and their powers) have the range in the Jacobson radical is considered. The proofs are based on the density theorem for derivations.
LA - eng
KW - derivations; Jacobson radical; Banach algebras
UR - http://eudml.org/doc/216692
ER -
References
top- [1] B. Aupetit, A Primer on Spectral Theory, Springer, 1991.
- [2] K. I. Beidar and M. Brešar, Extended Jacobson density theorem for rings with derivations and automorphisms, submitted. Zbl1003.47029
- [3] K. I. Beidar, W. S. Martindale III and A. V. Mikhalev, Rings with Generalized Identities, Marcel Dekker, 1996.
- [4] M. Brešar, Derivations on noncommutative Banach algebras II, Arch. Math. (Basel) 61 (1994), 56-59.
- [5] M. Brešar, Derivations mapping into the socle, II, Proc. Amer. Math. Soc. 126 (1998), 181-188.
- [6] M. Brešar and P. Šemrl, On locally linearly dependent operators and derivations, Trans. Amer. Math. Soc. 351 (1999), 1257-1275. Zbl0920.15009
- [7] L. O. Chung and J. Luh, Nilpotency of derivations, Canad. Math. Bull. 26 (1983), 341-346. Zbl0476.16028
- [8] B. Felzenszwalb and C. Lanski, On the centralizers of ideals and nil derivations, J. Algebra 83 (1983), 520-530. Zbl0519.16022
- [9] I. N. Herstein, A note on derivations, Canad. Math. Bull. 21 (1978), 369-370. Zbl0412.16018
- [10] I. N. Herstein, Sui commutatori degli anelli semplici, Rend. Sem. Mat. Fis. Milano 33 (1963), 80-86.
- [11] V. K. Kharchenko, Differential identities of prime rings, Algebra and Logic 17 (1978), 155-168. Zbl0423.16011
- [12] C. Lanski, Derivations nilpotent on subsets of prime rings, Comm. Algebra 20 (1992), 1427-1446. Zbl0759.16014
- [13] C. Lanski, An Engel condition with derivation, Proc. Amer. Math. Soc. 118 (1993), 731-734. Zbl0821.16037
- [14] C. Le Page, Sur quelques conditions entraȋnant la commutativité dans les algèbres de Banach, C. R. Acad. Sci. Paris Sér. A 265 (1967), 235-237. Zbl0158.14102
- [15] W. S. Martindale III and C. R. Miers, On the iterates of derivations of prime rings, Pacific J. Math. 104 (1983), 179-190. Zbl0507.16022
- [16] M. Mathieu, Where to find the image of a derivation, in: Banach Center Publ. 30, Inst. Math. Polish Acad. Sci., Warszawa, 1994, 237-249. Zbl0813.47043
- [17] M. Mathieu and G. J. Murphy, Derivations mapping into the radical, Arch. Math. (Basel) 57 (1991), 469-474. Zbl0714.46038
- [18] M. Mathieu and V. Runde, Derivations mapping into the radical, II, Bull. London Math. Soc. 24 (1992), 485-487. Zbl0733.46023
- [19] G. J. Murphy, Aspects of the theory of derivations, in: Banach Center Publ. 30 1994, 267-275. Zbl0811.46045
- [20] V. Pták, Commutators in Banach algebras, Proc. Edinburgh Math. Soc. 22 (1979), 207-211. Zbl0407.46043
- [21] V. Runde, Range inclusion results for derivations on noncommutative Banach algebras, Studia Math. 105 (1993), 159-172. Zbl0810.46044
- [22] A. M. Sinclair, Continuous derivations on Banach algebras, Proc. Amer. Math. Soc. 20 (1969), 166-170.
- [23] I. M. Singer and J. Wermer, Derivations on commutative normed algebras, Math. Ann. 129 (1955), 260-264. Zbl0067.35101
- [24] M. P. Thomas, The image of a derivation is contained in the radical, Ann. of Math. 128 (1988), 435-460. Zbl0681.47016
- [25] Yu. V. Turovskiĭ and V. S. Shul'man, Conditions for the massiveness of the range of a derivation of a Banach algebra and of associated differential operators, Mat. Zametki 42 (1987), 305-314 (in Russian).
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