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A B.A.I. proof of the non-Arens regularity of 
Author(s):
Colin
C.
Graham
Journal:
Proc. Amer. Math. Soc.
133
(2005),
163-165.
MSC (2000):
Primary 43A10, 46H99, 46B10
Posted:
July 26, 2004
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Abstract:
The non-Arens regularity of  is proved for all non-discrete groups and all amenable groups. The proof uses bounded approximate identities in an elementary way.
References:
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- 1.
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- P. Civin and B. Yood, The second conjugate space of a Banach algebra as an algebra, Pacific J. Math. 11, 1961, 847-870. MR 0143056 (26:622)
- 3.
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- 7.
- E. E. Granirer, Day points for quotients of the Fourier algebra
 , extreme nonergodicity of their duals and extreme non-Arens regularity, Illinois J. Math. 40, (No.3), 1996, 402-419. MR 1407625 (98c:43005) - 8.
- J.-P. Pier, Amenable Locally Compact Groups, John Wiley & Sons, New York, 1984.MR 0767264 (86a:43001)
- 9.
- A. Ülger, Arens regularity of weakly sequentially complete Banach algebras, Proc. Amer. Math. Soc. 127, 1999, 3221-3227. MR 1605953 (2000b:46080)
- 10.
- N. J. Young, The irregularity of multiplication in group algebras, Quarterly J. Math. (2) 24, 1973, 59-62. MR 0320756 (47:9290)
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Additional Information:
Colin
C.
Graham
Affiliation:
Department of Mathematics, University of British Columbia (\textit{Mailing address}: RR\#1--H-46, Bowen Island, British Columbia, Canada V0N 1G0)
Email:
ccgraham@alum.mit.edu
DOI:
10.1090/S0002-9939-04-07600-2
PII:
S 0002-9939(04)07600-2
Keywords:
Arens regularity,
bounded approximate identity,
Day point,
locally compact group
Received by editor(s):
September 10, 2003
Posted:
July 26, 2004
Communicated by:
Andreas Seeger
Copyright of article:
Copyright
2004,
American Mathematical Society
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