A characterization of approximately inner automorphisms of AW*-factor of type II₁

Authors

Dmitriy Kim, National University of Uzbekistan, Tashkent, UzbekistanFollow

Abstract

Approximately inner *-automorphisms of AW*-algebra of type II₁ are considered. Faithful normalized quasitraces of AW*-algebras are studied and the inequality connecting ||.||₁ and ||.||₂ norms generated by quasitrace is obtained. It is showed the characterization of approximately inner *-automorphisms of AW*-algebra of type II₁.

First Page

16

Last Page

27

References

1. Connes A. Classication of injective facteurs. Ann. Math. Vol. 104, No. 1, pp. 73-115 (1976).

2. Stormer E. Real structure in the hyperfinite factor. Duke mathematical journal. Vol. 47, No. 1 (1980).

3. Li B.R. Introduction to Operator Algebras. World Sci. Singapore, pp. 237-256 (1992).

4. Li B.R. Real operator algebras. World Scientific Publishing Co. Pte. Ltd., 241 p. (2003).

5. Haagerup U. Quasitraces on exact C*-algebras are traces. C. R. Math. Acad. Sci. Soc. R. Can. 36(2-3), pp. 67–92 (2014).

6. Arzikulov F.N. On abstract JW-algebras. Sib. Math. J. 39, pp. 20–27 (1998).

7. Stormer E. On anti-automorphisms of von Neumann algebras. Pacific J. Math. 21, pp. 349-370(1967).

8. Berberian S. Baer *-rings. Die Grundlehren der mathematischen Wissenschaften, Springer-Verlag Berlin Heidelberg (1972).

9. Blackadar B. and Handelman D. Dimension functions and traces on C*-algebra. J. Funct. Anal. 45, pp. 297-340 (1982).

10. Ayupov Sh.A., Rakhimov A.A. Real W*-algebras. Actions of groups and Index theory for real factors. VDM Publishing House Ltd. Beau-Bassin, Germany, Bonn. 138 p. (2010).

Recommended Citation

Kim, Dmitriy (2023) "A characterization of approximately inner automorphisms of AW*-factor of type II₁," Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol. 6: Iss. 1, Article 2.
DOI: https://doi.org/10.56017/2181-1318.1235