Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On local automorphisms of group algebras
of compact groups


Authors: Lajos Molnár and Borut Zalar
Journal: Proc. Amer. Math. Soc. 128 (2000), 93-99
MSC (1991): Primary 43A15, 43A22, 46H99
DOI: https://doi.org/10.1090/S0002-9939-99-05108-4
Published electronically: June 30, 1999
MathSciNet review: 1637412
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that with few exceptions every local isometric automorphism of the group algebra $L^p(G)$ of a compact metric group $G$ is an isometric automorphism.


References [Enhancements On Off] (What's this?)

  • [BaMo] C.J.K. Batty and L. Molnár, On topological reflexivity of the groups of *-automorphisms and surjective isometries of $B(H)$, Arch. Math. 67 (1996), 415-421. MR 97f:47034
  • [Bre] M. Bre\v{s}ar, Characterizations of derivations on some normed algebras with involution, J. Algebra 152 (1992), 454-462. MR 94e:46098
  • [BrSe1] M. Bre\v{s}ar and P. \v{S}emrl, Mappings which preserve idempotents, local automorphisms, and local derivations, Canad. J. Math. 45 (1993), 483-496. MR 94k:47054
  • [BrSe2] M. Bre\v{s}ar and P. \v{S}emrl, On local automorphisms and mappings that preserve idempotents, Studia Math. 113 (1995), 101-108. MR 96i:47058
  • [Cri] R.L. Crist, Local derivations on operator algebras, J. Funct. Anal. 135 (1996), 76-92. MR 96m:46128
  • [HeRo] E. Hewitt and K.A. Ross, Abstract Harmonic Analysis I., II., Springer Verlag, 1963, 1970. MR 28:158; MR 41:7378
  • [Kad] R.V. Kadison, Local derivations, J. Algebra 130 (1990), 494-509. MR 91f:46092
  • [Lar] D.R. Larson, Reflexivity, algebraic reflexivity and linear interpolation, Amer. J. Math. 110 (1988), 283-299. MR 89d:47096
  • [LaSo] D.R. Larson and A.R. Sourour, Local derivations and local automorphisms of $B(X)$, in Proc. Sympos. Pure Math. 51, Part 2, Providence, Rhode Island, 1990, 187-194. MR 91k:47106
  • [Mol1] L. Molnár, Algebraic difference between $p$-classes of an $H^*$-algebra, Proc. Amer. Math. Soc. 124 (1996), 169-175. MR 96d:46072
  • [Mol2] L. Molnár, The set of automorphisms of $B(H)$ is topologically reflexive in $B(B(H))$, Studia Math. 122 (1997), 183-193. MR 98e:47068
  • [Mol3] L. Molnár, Reflexivity of the automorphism and isometry groups of $C^*$-algebras in BDF theory, Arch. Math., to appear.
  • [Mol4] L. Molnár and M. Gy\H{o}ry, Reflexivity of the automorphism and isometry groups of the suspension of $B(H)$, J. Funct. Anal. 159 (1998), 568-586. CMP 99:04
  • [RuDy] B. Russo and H.A. Dye, A note on unitary operators in $C^*$-algebras, Duke Math. J. 33 (1966), 413-416. MR 33:1750
  • [Sco] W.R. Scott, Half-homomorphisms of groups, Proc. Amer. Math. Soc. 8 (1957), 1141-1144. MR 20:2388
  • [Shu] V.S. Shul'man, Operators preserving ideals in $C^*$-algebras, Studia Math. 109 (1994), 67-72. MR 95b:46097
  • [Str] R.S. Strichartz, Isomorphisms of group algebras, Proc. Amer. Math. Soc. 17 (1966), 858-862. MR 33:1751
  • [ZhXi] J. Zhu and C. Xiong, Bilocal derivations of standard operator algebras, Proc. Amer. Math. Soc. 125 (1997), 1367-1370. MR 97g:46091

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 43A15, 43A22, 46H99

Retrieve articles in all journals with MSC (1991): 43A15, 43A22, 46H99


Additional Information

Lajos Molnár
Affiliation: Institute of Mathematics, Lajos Kossuth University, 4010 Debrecen, P.O. Box 12, Hungary
Email: molnarl@math.klte.hu

Borut Zalar
Affiliation: Department of Basic Sciences, Faculty of Civil Engineering, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia
Email: borut.zalar@uni-mb.si

DOI: https://doi.org/10.1090/S0002-9939-99-05108-4
Keywords: Compact group, group algebra, isometric automorphism, local isometric automorphism
Received by editor(s): March 4, 1998
Published electronically: June 30, 1999
Additional Notes: This research was supported by the Joint Hungarian-Slovene research project supported by OMFB in Hungary and the Ministry of Science and Technology in Slovenia, Reg. No. SLO-2/96. The first author was supported in part by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. T–016846 F–019322, and by a grant from the Ministry of Education, Hungary, Reg. No. FKFP 0304/1997. The second author was supported in part by a grant from the Ministry of Science and Technology, Slovenia
Communicated by: David R. Larson
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society