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Jordan *-derivation pairs on a complex *-algebra

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Summary

The aim of this paper is to study the system of functional equations

$$\begin{gathered} E(x^3 ) = E(x)x*^2 + xF(x)x* + x^2 E(x) \hfill \\ F(x^3 ) = F(x)x*^2 + xE(x)x* + x^2 F(x) \hfill \\ \end{gathered} $$

, where is a complex *-algebra and are unknown additive functions. This problem arises naturally in connection with the question of representability of quadratic functionals via sesquilinear forms on modules over. We give a fairly complete solution of the problem and examine the case of some particular algebras.

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References

  1. F. F. Bonsall andJ. Duncan,Complete normed algebras, Springer, New York, 1973.

    MATH  Google Scholar 

  2. M. Bresar andJ. Vukman,On some additive mappings in rings, with involution, Aequationes Math.38 (1980), 178–185.

    Article  MathSciNet  Google Scholar 

  3. M. Brešar andB. Zalar,On the structure of Jordan *-derivations, Colloq. Math.63 (1992), 163–171.

    MathSciNet  MATH  Google Scholar 

  4. B. E. Johnson andA. M. Sinclair,Continuity of derivations and a problem of Kaplansky, Amer. J. Math.90 (1968), 1067–1073.

    Article  MATH  MathSciNet  Google Scholar 

  5. L. Molnár,The range of a Jordan *-derivation, Math. Japon44 (1996), 353–356.

    MATH  MathSciNet  Google Scholar 

  6. L. Molnár,On the range of a normal Jordan *-derivation, Comment. Math. Univ. Carolin.35 (1994), 691–695.

    MATH  MathSciNet  Google Scholar 

  7. G. J. Murphy,C *-algebras and operator theory, Academic Press, San Diego, 1990.

    Google Scholar 

  8. P. Šemrl,On quadratic and sesquilinear functions, Aequationes Math.19 (1986), 184–190.

    Google Scholar 

  9. P. Šemrl,On quadratic functions, Bull. Austral. Math. Soc.37 (1988), 27–29.

    Article  MathSciNet  MATH  Google Scholar 

  10. P. Šemrl,On Jordan *-derivations and an application, Colloq. Math.59 (1990), 241–251.

    MathSciNet  MATH  Google Scholar 

  11. P. Šemrl,Quadratic functions and Jordan *-derivations, Studia Math.97 (1991), 157–165.

    MathSciNet  MATH  Google Scholar 

  12. P. Šemrl,Quadratic and quasi-quadratic functionals, Proc. Amer. Math. Soc.119 (1993), 1105–1113.

    Article  MathSciNet  MATH  Google Scholar 

  13. P. Šemrl,Jordan *-derivations of standard operator algebras, Proc. Amer. Math. Soc.120 (1994), 515–518.

    Article  MathSciNet  MATH  Google Scholar 

  14. B. Zalar,Jordan *-derivations and quadratic functions on octonion algebras, Comm. Algebra22 (1994), 2845–2859.

    Article  MATH  MathSciNet  Google Scholar 

  15. B. Zalar,Jordan *-derivation pairs and quadratic functionals on modules over *-rings Aequationes Math.54 (1997), 31–43.

    Article  MATH  MathSciNet  Google Scholar 

  16. B. Zalar,Jordan-von Neumann theorem for Saworotnow’s generalized Hilbert space, Acta Math. Hungar.69 (1995), 301–325.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Lajos Kossuth University, P.O. Box 12, H-4010, Debrecen

    L. Molnár

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  1. L. Molnár
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Correspondence to L. Molnár.

Additional information

Research partially supported by the Hungarian National Research Science Foundation, Operating Grant Number OTKA 1652 and K&H Bank Ltd., Universitas Foundation.

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Molnár, L. Jordan *-derivation pairs on a complex *-algebra. Aequ. Math. 54, 44–55 (1997). https://doi.org/10.1007/BF02755445

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  • DOI: https://doi.org/10.1007/BF02755445

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