\(\xi\)-Lie Derivations on Algebras of Locally Measurable Operators

For citation:  Juraev I. M. \(\xi\)-Lie derivations on algebras of locally measurable operators // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 19, no. 1, pp. 26-35. DOI 10.23671/VNC.2016.1.5937

1. Albeverio S., Ayupov Sh. A., and Kudaybergenov K. K. Structure of derivations on various algebras of measurable operators for type \(I\) von Neumann algebras. J. Func. Anal. 2009. Vol. 256. P. 2917-2943.

2. Ayupov Sh. A., Kudaybergenov K. K. Additive derivations algebras of measurable operators. J. Operator Theory. 2012. Vol. 67, no 2. P. 101-116.

3. Juraev I. M. Structure of Lie deriv ations on algebras of measurable operators. Vladikavkazskij matematicheskij zhurnal [Vladikavkaz Math. J.] 2012. Vol. 14, no.3. P. 58-62. [Russian].

4. Kadison R. V., Ringrose J. R. Fundamentals of the Theory of Operator Algebras. Vol. I: Elementary Theory. N.Y. etc.: Acad. Press, 1983. 398 p.

5. Kusraev A. G. Automorphisms and derivations on a universally complete complex \(f\)-algebra. Siberian Math. J. 2006. Vol 47. P. 77-85.

6. Mathieu M., Villena A. R. The structure of Lie derivations on \(C^*\)-algebras. J. Func. Anal. 2003. Vol. 202. P. 504-525.

7. Muratov M. A., Chilin V. I. Algebras of Measurable and Locally Measurable Operators. Pratsi In-ty matematiki NAN Ukraini. Kyiv, 2007. Vol.69. 390 p.
[Russian].

8. Robert Miers C. Lie derivations of von Neumann algebras. Duke Math. J. 1973. Vol. 40. P. 403-409.

9. Sakai S. \(C^*\)-Algebras and \(W^{*}\)-Algebras. N.Y.-Heidelberg--Berlin: Springer-Verlag, 1971.

10. Segal I. A non-commutative extention of abstract integration. Ann. Math. 1953. Vol. 57. P. 401-457.

11. Chilin V. I., Juraev I. M. Commutatores of locally measurable operators affiliated with a von Neumann algebra type I. Materialy Respublikanskoj nauch. konf. [Materials of the Republican scientific. Conf.]. Urgench, 2012. Vol. 2. P. 122-124.

12. Chilin V. I., Juraev I. M. Additive Lie derivations on algebras locally measurable operators. Materialy Respublikanskoj nauch. konf. [Materials of the Republican scientific. Conf.]. Tashkent, 2013. P. 256-258.