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A note on Automatic continuity of \((\psi , \phi)\)-derivations

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Abstract

The main purpose of this paper is to present the conditions under which every \((\psi , \phi)\)-derivation is continuous on topological algebras such as normed algebras, Banach algebras and \(C^{*}\)-algebras.

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References

  1. Bade, W.G., Curtis, P.C.: Homomorphisms of commutative Banach algebras. Am. J. Math. 82, 589–608 (1960)

    Article  MATH  Google Scholar 

  2. Dales, H.D.: Banach Algebras and Automatic Continuity, London Mathematical Society Monographs. New Series, vol. 24. Oxford Science Publications, The Clarendon Press, Oxford University Press, New York (2000)

  3. Dales, H.D.: Automatic continuity: a survey. Bull. Lond. Math. Soc. 10(2), 129–183 (1978)

    Article  MATH  Google Scholar 

  4. Hosseini, A., Hassani, M., Niknam, A., Hejazian, S.: Some results on \(\sigma\)-Derivations. Ann. Funct. Anal. 2, 75–84 (2011)

    Article  MATH  Google Scholar 

  5. Hosseini, A., Hassani, M., Niknam, A.: Generalized \(\sigma\)-derivation on Banach algebras. Bull. Iranian. Math. Soc. 37, 81–94 (2011)

    MATH  Google Scholar 

  6. Hosseini, A.: On the image, characterization, and automatic continuity of \((\sigma, \tau )\)-derivations. Arch. Math. 109, 461–469 (2017)

    Article  MATH  Google Scholar 

  7. Hosseini, A., Hassani, M.: Some achievements on two variable -derivations. J. Math. Ext. 8(4), 93–108 (2014)

    MATH  Google Scholar 

  8. Hejazian, S., Janfada, A.R., Mirzavaziri, M., Moslehian, M.S.: Achivement of continuity of \((\phi,\psi )\)-derivations. Bull. Belg. Math. Soc. Simon Stevn. 14, 641–652 (2007)

    MATH  Google Scholar 

  9. Hou, C., Ming, Q.: Continuity of \((\alpha, \beta )\)-derivations of operator algebras. J. Korean Math. Soc. 48, 823–835 (2011)

    Article  Google Scholar 

  10. Johnson, B.E., Sinclair, A.M.: Continuity of derivations and a problem of Kaplansky. Am. J. Math. 90, 1067–1073 (1968)

    Article  MATH  Google Scholar 

  11. Kaplansky, I.: Functional Analysis, Some Aspects of Analysis and Probability, Surveys in Applied Mathematics. vol. 4. London (1958)

  12. Mirzavaziri, M., Moslehian, M.S.: Automatic continuity of \(\sigma\)-derivations in \(C^{\ast }\)-algebras. Proc. Am. Math. Soc. 134, 3319–3327 (2006)

    Article  MATH  Google Scholar 

  13. Ringrose, J.R.: Automatic continuity of derivations of operator algebras. J. Lond. Math. Soc. 5(2), 432–438 (1972)

    Article  MATH  Google Scholar 

  14. Sinclair, A. M.: Automatic Continuity of Linear Operators. London Mathematical Society. Lecture Note Series, vol. 21. Cambridge University Press, Cambridge (1976)

  15. Sakai, S.: On a conjecture of Kaplansky. T\(\hat{o}\)hoku Math. J. 12, 31–33 (1960)

  16. Villena, A.R.: Automatic continuity in associative and nonassociative context. Irish Math. Soc. Bull. 46, 43–76 (2001)

    Article  MATH  Google Scholar 

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Acknowledgements

The author thanks the referee for his/her careful reading of the paper and suggesting valuable comments that improved the quality of this work. Moreover, this research has been supported by a grant from Kashmar Higher Education Institute [grant number 28/1348/1400/578].

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  1. Kashmar Higher Education Institute, Kashmar, Iran

    Amin Hosseini

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  1. Amin Hosseini
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Correspondence to Amin Hosseini.

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Hosseini, A. A note on Automatic continuity of \((\psi , \phi)\)-derivations. Rend. Circ. Mat. Palermo, II. Ser 72, 71–79 (2023). https://doi.org/10.1007/s12215-021-00661-3

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