Hostname: page-component-7dd5485656-zklqj Total loading time: 0 Render date: 2025-10-29T16:20:12.305Z Has data issue: false hasContentIssue false
  • English
  • Français

2-LOCAL DERIVATIONS ON SEMI-FINITE VON NEUMANN ALGEBRAS

Published online by Cambridge University Press:  25 February 2013

SHAVKAT AYUPOV  and
FARKHAD ARZIKULOV
SHAVKAT AYUPOV
Affiliation:
Institute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan, and the Abdus Salam International Centre for Theoretical Physics (ICTP) Trieste, Italy e-mail: sh_ayupov@mail.ru
FARKHAD ARZIKULOV
Affiliation:
Institute of Mathematics, National University of Uzbekistan, Tashkent, and Andizhan State University, Andizhan, Uzbekistan e-mail: arzikulovfn@rambler.ru
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In the present paper we prove that every 2-local derivation on a semi-finite von Neumann algebra is a derivation.

Keywords

Primary 46L57Secondary 46L40

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 1 , January 2014 , pp. 9 - 12
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

REFERENCES

1.Sh., A. Ayupov and Arzikulov, F. N., 2-local derivations on von Neumann algebras of type I. Available at http://www.arxiv.org v1 [math.OA], accessed 29 December 2011.Google Scholar
2.Sh., A. Ayupov and Kudaybergenov, K. K., 2-local derivations and automorphisms on B(H), J. Math. Anal. Appl. 395 (2012), 15–18.Google Scholar
3.Sh., A. Ayupov, Kudaybergenov, K. K., Nurjanov, B. O. and Alauatdinov, A. K., Local and 2-local derivations on noncommutative Arens algebras, Mathematica Slovaca (to appear). Available at http://arxiv.org/abs/1110.1557, accessed 7 October 2011.Google Scholar
4.Bresar, M., Jordan derivations on semiprime rings, Proc. Amer. Math. Soc. 104 (1988), 1003–1006.Google Scholar
5.Kim, S. O. and Kim, J. S., Local automorphisms and derivations on Mn, Proc. Amer. Math. Soc. 132 (2004), 1389–1392.Google Scholar
6.Lin, Y. and Wong, T., A note on 2-local maps, Proc. Edinb. Math. Soc. 49 (2006), 701–708.Google Scholar
7.Šemrl, P., Local automorphisms and derivations on B(H), Proc. Amer. Math. Soc. 125 (1997), 2677–2680.Google Scholar
8.Takesaki, M., Theory of operator algebras I. (Springer-Verlag, New York, 1979).Google Scholar