Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Local automorphisms and derivations on certain $C^*$-algebras

Author(s): Sang Og Kim; Ju Seon Kim
Journal: Proc. Amer. Math. Soc. 133 (2005), 3303-3307.
MSC (2000): Primary 47B49, 47L30
Posted: June 20, 2005
Retrieve article in: PDF DVI PostScript

Abstract | References | Similar articles | Additional information

Abstract: It is shown that continuous $2$-local derivations on $\operatorname{AF}$ $C^*$-algebras are derivations and surjective $2$-local *-automorphisms on prime $C^*$-algebras or on $C^*$-algebras such that the identity element is properly infinite are *-automorphisms.

References:

[BaMo]
C. J. K. Batty and L. Molnár, On topological reflexivity of the groups of *-automorphisms and surjective isometries of $\mathcal{B}(\mathcal{H})$, Arch. Math. 67 (1996), 415-421. MR 1411996 (97f:47034)

[BrSe]
M. Bresar and P. Semrl, On local automorphisms and mappings that preserve idempotents, Studia Math. 113 (1995), 101-108. MR 1318418 (96i:47058)

[Cri]
R. L. Crist, Local derivations on operator algebras, J. Funct. Anal., 135 (1996), 76-92. MR 1367625 (96m:46128)

[Davi]
K. R. Davidson, $C^*$-algebras by example, Field Institute Monographs, 6 (1996). MR 1402012 (97i:46095)

[Her]
I. N. Herstein, Topics in ring theory, Chicago Lectures in Mathematics, The University of Chicago Press (1965). MR 0271135 (42:6018)

[Kad]
R. V. Kadison, Local derivations, J. Algebra, 130 (1990), 494-509. MR 1051316 (91f:46092)

[Kim2]
S. O. Kim and J. S. Kim, Local automorphisms and derivations on $M_n$, Proc. Amer. Math. Soc., 132 (2004), 1389-1392. MR 2053344 (2005b:47074)

[KoSl]
S. Kowalski and Z. Slodkowski, A characterization of multiplicative linear functionals in Banach algebras, Studia Math., 67 (1980), 215-223. MR 0592387 (82d:46070)

[LaSo]
D. R. Larson and A. R. Sourour, Local derivations and local automorphisms of $B(X)$, Proc. Sympos. Pure Math. 51, Part 2, Providence, Rhode Island (1990), 187-194. MR 1077437 (91k:47106)

[MaUl]
S. Mazur and S. Ulam, Sur les transformations isométriques d'espaces vectoriels normés, C. R. Acad. Sci. Paris, 194 (1932), 946-948.

[Mol]
L. Molnár, Local automorphisms of operator algebras on Banach spaces, Proc. Amer. Math. Soc., 131 (2003), 1867-1874. MR 1955275 (2003j:47050)

[Sem]
P. Semrl, Local automorphisms and derivations on $B(H)$, Proc. Amer. Math. Soc., 125 (1997), 2677-2680. MR 1415338 (98e:46082)

[Sto]
E. Størmer, On the Jordan structure of $C^*$-algebras, Trans. Amer. Math. Soc., 120 (1965), 438-447. MR 0185463 (32:2930)

[XiLu]
J. Xie and F. Lu, A note on $2$-local automorphisms of digraph algebras, Linear Algebra Appl., 378 (2004), 93-98. MR 2031786 (2004k:47069)

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47B49, 47L30

Retrieve articles in all Journals with MSC (2000): 47B49, 47L30

Additional Information:

Sang Og Kim
Affiliation: Department of Mathematics, Hallym University, Chuncheon 200-702, Korea
Email: sokim@hallym.ac.kr

Ju Seon Kim
Affiliation: Department of Mathematics Education, Seoul National University, Seoul, 151-742, Korea

DOI: 10.1090/S0002-9939-05-08059-7
PII: S 0002-9939(05)08059-7
Keywords: $2$-local derivation, $2$-local *-automorphism, $\operatorname{AF}$ $C^*$-algebra, prime $C^*$-algebra
Received by editor(s): June 16, 2004
Posted: June 20, 2005
Additional Notes: This work was supported by a Research Grant from Hallym University, Korea
Communicated by: David R. Larson
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google