Weak amenability of Segal algebras

Authors:
H. G. Dales and S. S. Pandey

Journal:
Proc. Amer. Math. Soc. **128** (2000), 1419-1425

MSC (1991):
Primary 46J10

DOI:
https://doi.org/10.1090/S0002-9939-99-05139-4

Published electronically:
October 6, 1999

MathSciNet review:
1641681

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a locally compact abelian group, and let . We show that the Segal algebra is always weakly amenable, but that it is amenable only if is discrete.

**[1]**W. G. Bade, P. C. Curtis and H. G. Dales,*Amenability and weak amenability for Beurling and Lipschitz algebras*, Proc. London Math.Soc., (3)**55**(1987), 359-377. MR**88f:46098****[2]**J. T. Burnham,*Closed ideals in subalgebras of Banach algebras I*, Proc. American Math. Soc.,**32**(1972), 551-555. MR**45:4146****[3]**H. G. Dales,*Banach algebras and automatic continuity*, Clarendon Press, Oxford, to appear.**[4]**M. Despi\'{c} and F. Ghahramani,*Weak amenability of group algebras of locally compact groups*, Canadian Math. Bulletin,**37**(1994), 165-167. MR**95c:43003****[5]**J. E. Galé,*Weak amenability of Banach algebras generated by some analytic semigroups*, Proc. American Math. Soc.,**104**(1988), 546-550. MR**90a:46144****[6]**N. Grønbæk,*A characterization of weakly amenable Banach algebras*, Studia Math.,**94**(1989), 149-162. MR**92a:46055****[7]**A. Ya. Helemskii,*The homology of Banach and topological algebras*, Kluwer Academic Publishers, Dordrecht, 1989. MR**92d:46178****[8]**E. Hewitt and K. A. Ross,*Abstract harmonic analysis, Vol. I*, Springer-Verlag, Berlin, 1963. MR**28:158****[9]**B. E. Johnson,*Cohomology in Banach algebras*, Memoir American Math. Soc,**127**(1972). MR**51:11130****[10]**R. Larsen, T. S. Liu and J. K. Wang,*On functions with Fourier transforms in*, Michigan Math. J,**11**(1964), 369-378. MR**30:412****[11]**J. C. Martin and L. Y. H. Yap,*The algebra of functions with Fourier transforms in*, Proc. American Math. Soc,**24**(1970), 217-219. MR**40:646****[12]**S. Poornima,*Multipliers of Sobolev spaces*, J.Functional Analysis,**45**(1982), 1-28. MR**83c:46033****[13]**H. Reiter,*Classical harmonic analysis and locally compact groups*, Oxford University Press, 1968. MR**46:5933****[14]**H. Reiter, -*algebra and Segal algebras*, Springer-Verlag, 1971. MR**55:13158****[15]**W. Rudin,*Fourier analysis on groups*, J. Wiley, New York, 1962. MR**27:2808****[16]**A. M. Sinclair,*Continuous semigroups in Banach algebras*, London Math. Soc.Lecture Note Series,**63**, Cambridge University Press, 1982. MR**84b:46053****[17]**M. C. White,*Strong Wedderburn decompositions of Banach algebras containing analytic semigroups*, J. London Math. Soc. (2),**49**(1994), 331-342. MR**95d:46056**

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Additional Information

**H. G. Dales**

Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, England

Email:
pmt6hgd@leeds.ac.uk

**S. S. Pandey**

Affiliation:
Department of Mathematics, R. D. University, Jabalpur, India

Email:
ssp@rdunijb.ren.nic.in

DOI:
https://doi.org/10.1090/S0002-9939-99-05139-4

Received by editor(s):
March 10, 1998

Received by editor(s) in revised form:
July 3, 1998

Published electronically:
October 6, 1999

Additional Notes:
The second author acknowledges with thanks the support of the Royal Society-INSA exchange program which enabled him to visit the University of Leeds to work with the first author. He is also thankful to the Department of Pure Mathematics at Leeds for hospitality.

Communicated by:
Christopher D. Sogge

Article copyright:
© Copyright 2000
American Mathematical Society