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Solution to Farhadi-Ghahramani's multiplier problem
Author:
Matthias Neufang
Journal:
Proc. Amer. Math. Soc. 138 (2010), 553-555
MSC (2000):
Primary 43A20, 43A22
Posted:
October 14, 2009
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Additional Information
Abstract: We answer, in the negative, the main question raised by H. Farhadi and F. Ghahramani in their article Involutions on the second duals of group algebras and a multiplier problem, Proc. Edinburgh Math. Soc. (2) 50 (2007), no. 1, 153-161.
- 1.
H.G. Dales, A.T.-M. Lau and D. Strauss, Banach algebras on semigroups and on their compactifications, to appear in: Memoirs of the American Mathematical Society, http://www.amsta.leeds.ac.uk/
 pmt6hgd/preprints/AMSseconddualsfinal1.pdf.
- 2.
J.
Duncan and S.
A. R. Hosseiniun, The second dual of a Banach algebra, Proc.
Roy. Soc. Edinburgh Sect. A 84 (1979), no. 3-4,
309–325. MR
559675 (81f:46057), http://dx.doi.org/10.1017/S0308210500017170
- 3.
H.
Farhadi and F.
Ghahramani, Involutions on the second duals of group algebras and a
multiplier problem, Proc. Edinb. Math. Soc. (2) 50
(2007), no. 1, 153–161. MR 2294009
(2008b:43004), http://dx.doi.org/10.1017/S0013091505000660
- 4.
Michael
Grosser, Algebra involutions on the bidual of a Banach
algebra, Manuscripta Math. 48 (1984), no. 1-3,
291–295. MR
753735 (85k:46058), http://dx.doi.org/10.1007/BF01169012
- 5.
Neil
Hindman and Dona
Strauss, Algebra in the Stone-Čech compactification, de
Gruyter Expositions in Mathematics, vol. 27, Walter de Gruyter &
Co., Berlin, 1998. Theory and applications. MR 1642231
(99j:54001)
- 6.
Alexander
S. Kechris, On the classification problem for rank 2 torsion-free
abelian groups, J. London Math. Soc. (2) 62 (2000),
no. 2, 437–450. MR 1783636
(2002h:20078), http://dx.doi.org/10.1112/S0024610700001411
- 7.
Anthony
To Ming Lau and Viktor
Losert, On the second conjugate algebra of
𝐿₁(𝐺) of a locally compact group, J. London
Math. Soc. (2) 37 (1988), no. 3, 464–470. MR 939122
(89e:43007), http://dx.doi.org/10.1112/jlms/s2-37.3.464
- 8.
Matthias
Neufang, On a conjecture by Ghahramani-Lau and related problems
concerning topological centres, J. Funct. Anal. 224
(2005), no. 1, 217–229. MR 2139110
(2006b:46063), http://dx.doi.org/10.1016/j.jfa.2004.11.007
- 9.
A.
Yu. Ol′shanskiĭ, On residualing homomorphisms and
𝐺-subgroups of hyperbolic groups, Internat. J. Algebra Comput.
3 (1993), no. 4, 365–409. MR 1250244
(94i:20069), http://dx.doi.org/10.1142/S0218196793000251
- 1.
- H.G. Dales, A.T.-M. Lau and D. Strauss, Banach algebras on semigroups and on their compactifications, to appear in: Memoirs of the American Mathematical Society, http://www.amsta.leeds.ac.uk/ pmt6hgd/preprints/AMSseconddualsfinal1.pdf.
- 2.
- J. Duncan and S.A.R. Hosseiniun, The second dual of a Banach algebra, Proc. Roy. Soc. Edinburgh Sect. A 84 (1979), no. 3-4, 309-325. MR 559675 (81f:46057)
- 3.
- H. Farhadi and F. Ghahramani, Involutions on the second duals of group algebras and a multiplier problem, Proc. Edinburgh Math. Soc. (2) 50 (2007), no. 1, 153-161. MR 2294009 (2008b:43004)
- 4.
- M. Grosser, Algebra involutions on the bidual of a Banach algebra, Manuscripta Math. 48 (1984), no. 1-3, 291-295. MR 753735 (85k:46058)
- 5.
- N. Hindman and D. Strauss, Algebra in the Stone-Čech Compactification. Theory and Applications, de Gruyter Expositions in Mathematics 27, Walter de Gruyter & Co., Berlin, 1998. MR 1642231 (99j:54001)
- 6.
- A.S. Kechris, On the classification problem for rank
 torsion-free abelian groups, J. London Math. Soc. (2) 62 (2000), 437-450. MR 1783636 (2002h:20078)
- 7.
- A.T.M. Lau and V. Losert, On the second conjugate algebra of
 of a locally compact group, J. London Math. Soc. (2) 37 (1988), 464-470. MR 939122 (89e:43007)
- 8.
- M. Neufang, On a conjecture by Ghahramani-Lau and related problems concerning topological centres, J. Funct. Anal. 224 (2005), no. 1, 217-229. MR 2139110 (2006b:46063)
- 9.
- A. Yu. Ol'shanskiĭ, On residualing homomorphisms and
 -subgroups of hyperbolic groups, Internat. J. Algebra Comput. 3 (1993), no. 4, 365-409. MR 1250244 (94i:20069)
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Additional Information
Matthias Neufang
Affiliation:
School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, K1S 5B6, Canada
Email:
mneufang@math.carleton.ca
DOI:
http://dx.doi.org/10.1090/S0002-9939-09-09778-0
PII:
S 0002-9939(09)09778-0
Keywords:
Arens products,
group algebras,
Stone-\v{C}ech compactification,
module homomorphisms,
topological centres.
Received by editor(s):
February 11, 2008
Posted:
October 14, 2009
Additional Notes:
The author was partially supported by NSERC. This support is gratefully acknowledged.
Communicated by:
Marius Junge
Article copyright:
© Copyright 2009 American Mathematical Society
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