Local automorphisms and derivations on

Authors:
Sang Og Kim and Ju Seon Kim

Translated by:

Journal:
Proc. Amer. Math. Soc. **132** (2004), 1389-1392

MSC (2000):
Primary 47B49, 15A60

Published electronically:
December 18, 2003

MathSciNet review:
2053344

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The aim of this note is to give a short proof that 2-local derivations on , the matrix algebra over the complex numbers are derivations and to give a shorter proof that 2-local *-automorphisms on are *-automorphisms.

**[BrSe]**Matej Brešar and Peter Šemrl,*On local automorphisms and mappings that preserve idempotents*, Studia Math.**113**(1995), no. 2, 101–108. MR**1318418****[Kad]**Richard V. Kadison,*Local derivations*, J. Algebra**130**(1990), no. 2, 494–509. MR**1051316**, 10.1016/0021-8693(90)90095-6**[KoSl]**S. Kowalski and Z. Słodkowski,*A characterization of multiplicative linear functionals in Banach algebras*, Studia Math.**67**(1980), no. 3, 215–223. MR**592387****[LaSo]**David R. Larson and Ahmed R. Sourour,*Local derivations and local automorphisms of ℬ(𝒳)*, Operator theory: operator algebras and applications, Part 2 (Durham, NH, 1988) Proc. Sympos. Pure Math., vol. 51, Amer. Math. Soc., Providence, RI, 1990, pp. 187–194. MR**1077437**, 10.1090/pspum/051.2/1077437**[MaMo]**Marvin Marcus and B. N. Moyls,*Linear transformations on algebras of matrices*, Canad. J. Math.**11**(1959), 61–66. MR**0099996****[Mol1]**Lajos Molnár,*2-local isometries of some operator algebras*, Proc. Edinb. Math. Soc. (2)**45**(2002), no. 2, 349–352. MR**1912644**, 10.1017/S0013091500000043**[Mol2]**L. Molnár,*Local automorphisms of operator algebras on Banach spaces*, arXiv:math.OA /0209059 (2002)**[Sem]**Peter Šemrl,*Local automorphisms and derivations on ℬ(ℋ)*, Proc. Amer. Math. Soc.**125**(1997), no. 9, 2677–2680. MR**1415338**, 10.1090/S0002-9939-97-04073-2

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
47B49,
15A60

Retrieve articles in all journals with MSC (2000): 47B49, 15A60

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:
http://dx.doi.org/10.1090/S0002-9939-03-07171-5

Keywords:
2-local *-automorphism,
2-local derivation

Received by editor(s):
September 10, 2002

Received by editor(s) in revised form:
November 20, 2002

Published electronically:
December 18, 2003

Additional Notes:
This work was supported by the Research Grant from Hallym University, Korea

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2003
American Mathematical Society