A reflexivity problem concerning the algebra
Author:
Lajos Molnár
Journal:
Proc. Amer. Math. Soc. 129 (2001), 531537
MSC (1991):
Primary 47B48, 47B49
Published electronically:
September 20, 2000
MathSciNet review:
1707156
Fulltext PDF Free Access
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Abstract: Let be a compact Hausdorff space and let be a separable Hilbert space. We prove that the group of all order automorphisms of the algebra is algebraically reflexive.
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 C.J.K. Batty and L. Molnár, On topological reflexivity of the groups of *automorphisms and surjective isometries of , Arch. Math. 67 (1996), 415421. MR 97f:47034
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 R.V. Kadison, A generalized Schwarz inequality and algebraic invariants for operator algebras, Ann. of Math. 56 (1952), 494503. MR 14:481c
 3.
 R.V. Kadison, Local derivations, J. Algebra 130 (1990), 494509. MR 91f:46092
 4.
 R.V. Kadison and J. Ringrose, Derivations and automorphisms of operator algebras, Comm. Math. Phys. 4 (1967), 3263. MR 34:6552
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 E.C. Lance, Automorphisms of certain operator algebras, Amer. J. Math. 91 (1969), 160174. MR 39:3324
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 L. Molnár, The set of automorphisms of is topologically reflexive in , Studia Math. 122 (1997), 183193. MR 98e:47068
 9.
 L. Molnár and P. Semrl, Order isomorphisms and triple isomorphisms of operator ideals and their reflexivity, Arch. Math. 69 (1997), 497506. MR 99a:47054
 10.
 L. Molnár and M. Gyory, Reflexivity of the automorphism and isometry groups of the suspension of , J. Funct. Anal. 159 (1998), 568586. CMP 99:04
 11.
 L. Molnár and B. Zalar, Reflexivity of the group of surjective isometries on some Banach spaces, Proc. Edinb. Math. Soc. 42 (1999), 1736. CMP 99:09
 12.
 L. Molnár and B. Zalar, On local automorphisms of group algebras of compact groups, Proc. Amer. Math. Soc. 128 (2000), 9399. CMP 98:16
 13.
 L. Molnár, Reflexivity of the automorphism and isometry groups of algebras in BDF theory, Arch. Math. (to appear)
 14.
 H. Radjavi and P. Rosenthal, On invariant subspaces and reflexive algebras, Amer. J. Math. 91 (1969), 683692. MR 40:4796
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 R. C. Walker, The StoneCech Compactification, Springer, 1974. MR 52:1595
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Additional Information
Lajos Molnár
Affiliation:
Institute of Mathematics, Lajos Kossuth University, 4010 Debrecen, P.O. Box 12, Hungary
Email:
molnarl@math.klte.hu
DOI:
http://dx.doi.org/10.1090/S0002993900056045
PII:
S 00029939(00)056045
Keywords:
Reflexivity,
order automorphism,
$C^*$algebra
Received by editor(s):
November 16, 1998
Received by editor(s) in revised form:
May 3, 1999
Published electronically:
September 20, 2000
Additional Notes:
This research was supported from the following sources: 1) Joint HungarianSlovene research project supported by OMFB in Hungary and the Ministry of Science and Technology in Slovenia, Reg. No. SLO2/96, 2) Hungarian National Foundation for Scientific Research (OTKA), Grant No. T–030082 F–019322, 3) a grant from the Ministry of Education, Hungary, Reg. No. FKFP 0304/1997
Communicated by:
David R. Larson
Article copyright:
© Copyright 2000
American Mathematical Society
