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Local automorphisms and derivations on $\mathbb{M}_n$

Author(s): Sang Og Kim; Ju Seon Kim
Journal: Proc. Amer. Math. Soc. 132 (2004), 1389-1392.
MSC (2000): Primary 47B49, 15A60
Posted: December 18, 2003
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Abstract: The aim of this note is to give a short proof that 2-local derivations on $M_n$, the $n\times n$ matrix algebra over the complex numbers are derivations and to give a shorter proof that 2-local *-automorphisms on $M_n$ are *-automorphisms.

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

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

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

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

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M. Marcus and B. N. Moyls, Linear transformations on algebras of matrices, Canad. J. Math. 11 (1959), 61-66. MR 20:6432

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L. Molnár, 2-local isometries of some operator algebras, Proc. Edinburgh Math. Soc. 45 (2002), 349-352. MR 2003e:47067

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L. Molnár, Local automorphisms of operator algebras on Banach spaces, arXiv:math.OA /0209059 (2002)

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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/S0002-9939-03-07171-5
PII: S 0002-9939(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
Posted: December 18, 2003
Additional Notes: This work was supported by the Research Grant from Hallym University, Korea
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2003, American Mathematical Society

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The following works have cited this article

D. R. Larson and A. R. Sourour, Local derivations and local automorphisms of B(X), Proc. Sympos. Pure Math. 51, Part II, Amer. Math. Soc., 1990, pp. 187-194. MR 91k:47106

M. Marcus and B. N. Moyls, Linear transformations on algebras of matrices, Canad. J. Math. 11 (1959), 61-66. MR 20:6432

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

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

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

L. Molnar, 2-local isometries of some operator algebras, Proc. Edinburgh Math. Soc. 45 (2002), 349-352. MR 2003e:47067

L. Molnar, Local automorphisms of operators algebras on Banach spaces, Proc. Amer. Math. Soc. 131 (2003), 1867-1874.

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