Previous |  Up |  Next

Article

Keywords:
local derivation; standard operator algebra; locally inner derivation; symmetric norm ideal
Summary:
It is proved that every locally inner derivation on a symmetric norm ideal of operators is an inner derivation.
References:
[1] M. Brešar, P. Šemrl: Mappings which preserve idempotents, local automorphisms and local derivations. Canad. J. Math. 45 (1993), 483-496. DOI 10.4153/CJM-1993-025-4 | MR 1222512
[2] P. R. Chernoff: Representations, automorphisms and derivations of some operator algebras. J. Funct. Anal. 12 (1973), 275-289. MR 0350442 | Zbl 0252.46086
[3] C. K. Fong C. R. Miers, A. R. Sourour: Lie and Jordan ideals of operators on Hilbert space. Proc. Amer. Math. Soc. 84 (1982), 516-520. DOI 10.1090/S0002-9939-1982-0643740-0 | MR 0643740
[4] P. R. Halmos: Hilbert Space Problem Book. D. Van Nostrand Company, Princeton, New York, 1967. MR 0208368 | Zbl 0144.38704
[5] R. V. Kadison: Local derivations. J. Algebra 130 (1990), 494-509. DOI 10.1016/0021-8693(90)90095-6 | MR 1051316 | Zbl 0751.46041
[6] D. R. Larson, A. R. Sourour: Local derivations and local automorphisms of B(X). Proc. Sympos. Pure Math. 51. Part 2, Providence, Rhode Island 1990, pp. 187-194. MR 1077437
[7] S. Sakai: Derivations of W*-algebras. Ann. Math. 83 (1966), 273-279. DOI 10.2307/1970432 | MR 0193528
[8] P. Šemrl: Additive derivations of some operator algebras. Illinois J. Math. 35 (1991), 234-240. DOI 10.1215/ijm/1255987893 | MR 1091440
[9] P. Šemrl: Ring derivations on standard operator algebras. J. Funct. Anal. 112 (1993), 318-324. DOI 10.1006/jfan.1993.1035 | MR 1213141
[10] B. Simon: Trace Ideals and Their Applications. Cambridge University Press, Cambridge, 1979. MR 0541149 | Zbl 0423.47001
Partner of
EuDML logo