Derivations on commutative Banach algebras
HTML articles powered by AMS MathViewer
- by A. Khosravi PDF
- Proc. Amer. Math. Soc. 84 (1982), 60-64 Request permission
Abstract:
Let $A$ be a commutative Banach algebra with radical $R$ and $D$ be a derivation on $A$. If $K = \{ x \in R:\;{\text {for every }}n \geqslant 1,\;{D^n}x \in R\}$, then $DA \subseteq R$ if and only if $K$ is closed.References
- G. R. Allan, Embedding the algebra of formal power series in a Banach algebra, Proc. London Math. Soc. (3) 25 (1972), 329โ340. MR 305071, DOI 10.1112/plms/s3-25.2.329
- Frank F. Bonsall and John Duncan, Complete normed algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 80, Springer-Verlag, New York-Heidelberg, 1973. MR 0423029
- Julian Cusack, Automatic continuity and topologically simple radical Banach algebras, J. London Math. Soc. (2) 16 (1977), no.ย 3, 493โ500. MR 461136, DOI 10.1112/jlms/s2-16.3.493
- H. G. Dales, Automatic continuity: a survey, Bull. London Math. Soc. 10 (1978), no.ย 2, 129โ183. MR 500923, DOI 10.1112/blms/10.2.129
- B. E. Johnson, Continuity of derivations on commutative algebras, Amer. J. Math. 91 (1969), 1โ10. MR 246127, DOI 10.2307/2373262
- Nicholas P. Jewell and Allan M. Sinclair, Epimorphisms and derivations on $L^1(0,1)$ are continuous, Bull. London Math. Soc. 8 (1976), no.ย 2, 135โ139. MR 402507, DOI 10.1112/blms/8.2.135
- R. J. Loy, Continuity of derivations on topological algebras of power series, Bull. Austral. Math. Soc. 1 (1969), 419โ424. MR 415334, DOI 10.1017/S0004972700042349
- A. M. Sinclair, Continuous derivations on Banach algebras, Proc. Amer. Math. Soc. 20 (1969), 166โ170. MR 233207, DOI 10.1090/S0002-9939-1969-0233207-X
- Allan M. Sinclair, Automatic continuity of linear operators, London Mathematical Society Lecture Note Series, No. 21, Cambridge University Press, Cambridge-New York-Melbourne, 1976. MR 0487371
- I. M. Singer and J. Wermer, Derivations on commutative normed algebras, Math. Ann. 129 (1955), 260โ264. MR 70061, DOI 10.1007/BF01362370
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 60-64
- MSC: Primary 46J05
- DOI: https://doi.org/10.1090/S0002-9939-1982-0633278-9
- MathSciNet review: 633278