International Journal of Nonlinear Analysis and Applications
On some maps into Banach algebras and Banach modules
Document Type : Research Paper
Author
Faculty of Mathematical Sciences and Statistics, Malayer University, P.O. Box 65719-95863, Malayer, Iran
Abstract
In this paper, we study some maps from a $C^*$-algebra into a Banach algebra or a Banach module. Under some conditions, by extending on unitization of Banach algebras, we prove that the maps defined into Banach algebras are homomorphisms and the others defined into Banach modules are derivations. Applications of our results in the context of $C^*$-algebras are also provided.
Keywords
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[2] R. Badora, On approximate derivations, Math. Inequal. Appl. 9 (2006) 167–1731.
[3] D.G. Bourgin, Approximately isometric and multiplicative transformations on continuous function rings, Duke Math. J. 16 (1949) 385–397.
[4] J. Brzd¸ek and A Fo˘sner, Remarks on the stability of Lie homomorphisms, J. Math. Anal. Appl. 400 (2013) 585–596.
[5] H. G. Dales, Banach Algebras and Automatic Continuity, Oxford, New York, 2000.
[6] M. Eshaghi and M. Filali, Arens regularity of module actions, Studia Math. 181 (2007) 237–254.
[7] M. Eshaghi Gordji and M. S. Moslehian, A trick for investigation of approximate derivations, Math. Commun. 15 (2010) 99–105.
[8] B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972).
[9] R. V. Kadison and J.R. Ringrose, Fundamentals of the Theory of Operator Algebras, Elementary Theory, Academic Press, New York, 1983.
[10] T. Miura, G. Hirasawa and S. E. Takahasi, A perturbation of ring derivations on Banach algebras, J. Math. Anal. Appl. 319 (2006) 522–530.
[11] J. R. Ringrose, Automatic continuity of derivations of operator algebras, J. Lond. Math. Soc. 5 (1972) 432–438.
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Volume 12, Issue 2
November 2021Pages 471-477
- Receive Date: 09 November 2020
- Accept Date: 12 April 2021