A B.A.I. proof of the non-Arens regularity of $L^1(\mathcal G)$
HTML articles powered by AMS MathViewer
- by Colin C. Graham PDF
- Proc. Amer. Math. Soc. 133 (2005), 163-165 Request permission
Abstract:
The non-Arens regularity of $L^1(\mathcal G)$ is proved for all non-discrete groups and all amenable groups. The proof uses bounded approximate identities in an elementary way.References
- Richard Arens, The adjoint of a bilinear operation, Proc. Amer. Math. Soc. 2 (1951), 839–848. MR 45941, DOI 10.1090/S0002-9939-1951-0045941-1
- Paul Civin and Bertram Yood, The second conjugate space of a Banach algebra as an algebra, Pacific J. Math. 11 (1961), 847–870. MR 143056, DOI 10.2140/pjm.1961.11.847
- H. G. Dales, Banach algebras and automatic continuity, London Mathematical Society Monographs. New Series, vol. 24, The Clarendon Press, Oxford University Press, New York, 2000. Oxford Science Publications. MR 1816726
- — and A. T. M. Lau, The second dual of Beurling algebras, Preprint, 2002.
- 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, DOI 10.1017/S0308210500017170
- Colin C. Graham, Arens regularity and weak sequential completeness for quotients of the Fourier algebra, Illinois J. Math. 44 (2000), no. 4, 712–740. MR 1804322
- Edmond E. Granirer, Day points for quotients of the Fourier algebra $A(G)$, extreme nonergodicity of their duals and extreme non-Arens regularity, Illinois J. Math. 40 (1996), no. 3, 402–419. MR 1407625
- Jean-Paul Pier, Amenable locally compact groups, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1984. A Wiley-Interscience Publication. MR 767264
- A. Ülger, Arens regularity of weakly sequentially complete Banach algebras, Proc. Amer. Math. Soc. 127 (1999), no. 11, 3221–3227. MR 1605953, DOI 10.1090/S0002-9939-99-04894-7
- N. J. Young, The irregularity of multiplication in group algebras, Quart. J. Math. Oxford Ser. (2) 24 (1973), 59–62. MR 320756, DOI 10.1093/qmath/24.1.59
Additional Information
- Colin C. Graham
- Affiliation: Department of Mathematics, University of British Columbia (Mailing address: RR#1–H-46, Bowen Island, British Columbia, Canada V0N 1G0)
- Email: ccgraham@alum.mit.edu
- Received by editor(s): September 10, 2003
- Published electronically: July 26, 2004
- Communicated by: Andreas Seeger
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 163-165
- MSC (2000): Primary 43A10, 46H99, 46B10
- DOI: https://doi.org/10.1090/S0002-9939-04-07600-2
- MathSciNet review: 2085165