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A reflexivity problem concerning the  -algebra 
Author:
Lajos Molnár
Journal:
Proc. Amer. Math. Soc. 129 (2001), 531-537
MSC (1991):
Primary 47B48, 47B49
Posted:
September 20, 2000
MathSciNet review:
1707156
Full-text PDF Free Access
Abstract |
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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.
- 1.
Charles
J. K. Batty and Lajos
Molnár, On topological reflexivity of the groups of
∗-automorphisms and surjective isometries of
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no. 5, 415–421. MR 1411996
(97f:47034), http://dx.doi.org/10.1007/BF01189101
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V. Kadison, A generalized Schwarz inequality and algebraic
invariants for operator algebras, Ann. of Math. (2)
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(14,481c)
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(34 #6552)
- 5.
E.
C. Lance, Automorphisms of certain operator algebras, Amer. J.
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(39 #3324)
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283–299. MR
935008 (89d:47096), http://dx.doi.org/10.2307/2374503
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- 8.
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Math. 122 (1997), no. 2, 183–193. MR 1432168
(98e:47068)
- 9.
Lajos
Molnár and Peter
Šemrl, Order isomorphisms and triple isomorphisms of
operator ideals and their reflexivity, Arch. Math. (Basel)
69 (1997), no. 6, 497–506. MR 1480517
(99a:47054), http://dx.doi.org/10.1007/s000130050152
- 10.
L. Molnár and M. Gyory, Reflexivity of the automorphism and isometry groups of the suspension of
 , J. Funct. Anal. 159 (1998), 568-586. 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), 17-36. CMP 99:09
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L. Molnár and B. Zalar, On local automorphisms of group algebras of compact groups, Proc. Amer. Math. Soc. 128 (2000), 93-99. CMP 98:16
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- 1.
- C.J.K. Batty and L. Molnár, On topological reflexivity of the groups of *-automorphisms and surjective isometries of
 , Arch. Math. 67 (1996), 415-421. MR 97f:47034
- 2.
- R.V. Kadison, A generalized Schwarz inequality and algebraic invariants for operator algebras, Ann. of Math. 56 (1952), 494-503. MR 14:481c
- 3.
- R.V. Kadison, Local derivations, J. Algebra 130 (1990), 494-509. MR 91f:46092
- 4.
- R.V. Kadison and J. Ringrose, Derivations and automorphisms of operator algebras, Comm. Math. Phys. 4 (1967), 32-63. MR 34:6552
- 5.
- E.C. Lance, Automorphisms of certain operator algebras, Amer. J. Math. 91 (1969), 160-174. MR 39:3324
- 6.
- D.R. Larson, Reflexivity, algebraic reflexivity and linear interpolation, Amer. J. Math. 110 (1988), 283-299. MR 89d:47096
- 7.
- D.R. Larson and A.R. Sourour, Local derivations and local automorphisms of
 , in Proc. Sympos. Pure Math. 51, Part 2, Providence, Rhode Island 1990, 187-194. MR 91k:47106
- 8.
- L. Molnár, The set of automorphisms of
 is topologically reflexive in  , Studia Math. 122 (1997), 183-193. MR 98e:47068
- 9.
- L. Molnár and P. Semrl, Order isomorphisms and triple isomorphisms of operator ideals and their reflexivity, Arch. Math. 69 (1997), 497-506. 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), 568-586. 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), 17-36. CMP 99:09
- 12.
- L. Molnár and B. Zalar, On local automorphisms of group algebras of compact groups, Proc. Amer. Math. Soc. 128 (2000), 93-99. 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), 683-692. MR 40:4796
- 15.
- R. C. Walker, The Stone-Cech 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/S0002-9939-00-05604-5
PII:
S 0002-9939(00)05604-5
Keywords:
Reflexivity,
order automorphism,
$C^*$-algebra
Received by editor(s):
November 16, 1998
Received by editor(s) in revised form:
May 3, 1999
Posted:
September 20, 2000
Additional Notes:
This research was supported from the following sources: 1) Joint Hungarian-Slovene research project supported by OMFB in Hungary and the Ministry of Science and Technology in Slovenia, Reg. No. SLO-2/96, 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
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