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Arens regularity of weakly sequentially complete Banach algebras


Author: A. Ülger
Journal: Proc. Amer. Math. Soc. 127 (1999), 3221-3227
MSC (1991): Primary 46G10, 46H20
DOI: https://doi.org/10.1090/S0002-9939-99-04894-7
Published electronically: April 27, 1999
MathSciNet review: 1605953
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Abstract: In this paper we prove the following result: Let $A$ be a nonunital Banach algebra with a bounded approximate identity. Then $A$ cannot be both Arens regular and weakly sequentially complete. The paper also contains some applications of this result.


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  • [B-D] F.F. Bonsall and J. Duncan, Complete normed algebras, Springer-Verlag (1973), New-York. MR 54:11013
  • [C-Y] I.G. Craw and N. Young, Regularity of multiplication in weighted group and semigroup algebras, Quart. J. Math. Oxford (2) 25 (1974), 351-381. MR 51:1282
  • [Cu-L] P. C. Curtis Jr. and R.J. Loy, The structure of amenable Banach algebras, J. London Math. Soc. (2) 40 (1989), 89-104. MR 90k:46114
  • [D] C.F. Dunkl, The measure algebra of a locally compact hypergroup, Trans. Amer. Math. Soc. 179 (1973), 331-348. MR 47:9171
  • [E] P. Eymard, L'Algebre de Fourier d'un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181-236. MR 37:4208
  • [F] B. Forrest, Amenability and the structure of the algebra $A_{p}(G),$ Trans. Amer. Math. Soc. 343 (1994), 233-243. MR 94g:43001
  • [G-R-W] J.E. Galé, T.J Ransford and M.C. White, Weakly compact homomorphisms, Trans. Amer. Math. Soc. 331 (1992), 815-824. MR 92h:46074
  • [H-R] E. Hewitt and K. Ross, Abstract Harmonic Analysis. Vol II, Springer-Verlag (1970), New-York. MR 41:7378
  • [J] R.I. Jewett, Spaces with an abstract convolution of measures, Advances in Math. 18 (1975), New-York. MR 52:14840
  • [L-W] A.T. Lau and J.C.S. Wong, Weakly almost periodic elements in $L_\infty(G)$ of a locally compact group, Proc. Amer. Math. Soc. 107 (1989), 1031-1036. MR 90m:43006
  • [U1] A. Ülger, Arens regularity sometimes implies the RNP, Pacific J. Math. 143 (1990), 377-399. MR 91f:46067
  • [U2] A. Ülger, Some results about the spectrum of commutative Banach algebras under the weak topology and applications, Monaths. Für Math. 121 (1996), 353-379. MR 98a:46058
  • [Y] N. Young, The irregularity of multiplication in group algebras, Quart. J. Math. Oxford (2) 24 (1973), 59-62. MR 47:9290

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Additional Information

A. Ülger
Affiliation: Department of Mathematics, Koç University, 80860 Istinye-Istanbul, Turkey
Email: aulger@ku.edu.tr

DOI: https://doi.org/10.1090/S0002-9939-99-04894-7
Keywords: Arens regularity, homomorphism
Received by editor(s): July 29, 1997
Received by editor(s) in revised form: January 22, 1998
Published electronically: April 27, 1999
Additional Notes: This work was supported by a fund of the Turkish Academy of Sciences.
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1999 American Mathematical Society

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