LOCAL DERIVATION OF REAL OPERATOR ALGEBRAS
DOI:
https://doi.org/10.46754/jmsi.2024.06.005Keywords:
real C*-algebra, real W*-algebra, local derivation, inner derivationAbstract
Local derivations of real W*-algebras are considered. Since in the self-adjoint part of the real W*-algebra a local derivation is studied in the same way as in the complex case, here we consider the skew-adjoint part of the real W*-algebra. In the case of factors, the final result has been obtained, namely, it has been proven that any local derivation of real (complex) factors is an inner derivation.
References
Kadison R. V. (1990). Local derivations. Journal of Algebra, 130, 494-509. DOI: https://doi.org/10.1016/0021-8693(90)90095-6
Johnson B. E. (2001). Local derivations on C*-algebras are derivations. Transactions of the American Mathematical Society, 353(1), 313-325. DOI: https://doi.org/10.1090/S0002-9947-00-02688-X
Karimov U. Sh. (2020). On the local derivations on real W*-algebras. Bulletin of the Institute of Mathematics.
Bresar M. (2007). Characterizing homomorphisms, derivations and multipliers in rings with idempotents. Proceeding of the Royal Society of Edinburg, 137(1), 9-21. https://doi.org/10.1017/S0308210504001088 DOI: https://doi.org/10.1017/S0308210504001088
Ayupov, Sh. A., Rakhimov, A. A., Usmanov, Sh. M. (1997). Jordan, real and lie structures in operator algebras (Vol. 418). Springer Dordrecht. DOI: https://doi.org/10.1007/978-94-015-8605-4
Ayupov Sh. A., & Rakhimov A. A. (2010). Real W*-algebras, actions of groups and index theory for real factors (pp. 138). VDM Publishing House Ltd. Beau-Bassin, Mauritius.
Kaplansky I. (1951). Projections in Banach algebras. Annals of Mathematics, 53, 235-249. DOI: https://doi.org/10.2307/1969540
Berberian S. K. (1972). Baer *-rings. Springer, Berlin. DOI: https://doi.org/10.1007/978-3-642-15071-5
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Journal of Mathematical Sciences and Informatics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
