References
F. F.Bonsall and J.Duncan, Complete normed algebras. Berlin-Heidelberg-New York 1973.
I. N. Herstein, Jordan derivations of prime rings. Proc. Amer. Math. Soc.8, 1104–1110 (1957).
I. Kaplansky, Functional analysis, in Some Aspects of Analysis and Probability. Surveys Appl. Math.4, 1–34, New York 1958.
D. C. Kleinecke, On operator commutators. Proc. Amer. Math. Soc.8, 535–536 (1957).
W. S. Martindale andC. R. Miers, On the iterates of derivations of prime rings. Pacific J. Math.104, 179–190 (1983).
E. C. Posner, Derivations in prime rings. Proc. Amer. Math. Soc.8, 1093–1100 (1957).
V. Pták, Commutators in Banach algebras. Proc. Edinburgh Math. Soc.22, 207–211 (1979).
F. V. Shirokov, Proof of a conjecture of Kaplansky. Uspekhi Mat. Nauk11, 167–168 (1956).
A. M. Sinclair, Continuous derivations on Banach algebras. Proc. Amer. Math. Soc.20, 166–170 (1969).
I. M. Singer andJ. Wermer, Derivations on commutative normed algebras. Math. Ann.129, 260–264 (1955).
M. P. Thomas, The image of a derivation is contained in the radical. Ann. Math.128, 435–460 (1988).
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Mathieu, M., Murphy, G.J. Derivations mapping into the radical. Arch. Math 57, 469–474 (1991). https://doi.org/10.1007/BF01246745
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DOI: https://doi.org/10.1007/BF01246745