SciELO - Scientific Electronic Library Online

 
vol.26 issue3QUASI - MACKEY TOPOLOGYA NOTE ON KKT-INVEXITY IN NONSMOOTH CONTINUOUS-TIME OPTIMIZATION author indexsubject indexarticles search
Home Pagealphabetic serial listing  

Services on Demand

Journal

Article

Indicators

Related links

Share


Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.26 no.3 Antofagasta Dec. 2007

http://dx.doi.org/10.4067/S0716-09172007000300004 

 

Proyecciones Journal of Mathematics
Vol. 26, Nº 3, pp. 259-267, December 2007.
Universidad Católica del Norte
Antofagasta - Chile


REGULARITY AND AMENABILITY OF THE SECOND DUAL OF WEIGHTED GROUP ALGEBRAS


A. REJALI ISFAHAN 1
H. R. E. VISHKI 2

1 Isfahan University, Irán
2 Ferdowsi University, Irán

Correspondencia a:



Abstract
For a wide variety of Banach algebras A (containing the group algebras L1(G), M (G) and A(G)) the Arens regularity of A** is equivalent to that A, and the amenability of A** is equivalent to the amenability and regularity of A. In this paper, among other things, we show that this variety contains the weighted group algebras L1(G, w) and M(G, w).


Key words : Arens product, Weighted group algebra, Amenability
MR(2000) Subject Classification : P46H25, 43A10.

REFERENCES
[A] Arens R.I.,“ The adjoint of a bilinear operation“, Proc. Amer. Math. Soc. 2, pp. 839-848,         [ Links ](1951).
[B] Baker J.W.,“ Measure algebras on semigroups“, The analytical and topological theory of semigroups, Walter de Gruyter, Berlin, New York, pp. 221-252,         [ Links ](1990).
[B-R] Baker J.W. and Rejali A.,“ On the Arens regularity of the weighted convolution algebras, J. London Math. Soc. (2) 40, pp. 535-546,         [ Links ](1987).
[D-G-H] Dales H.G., Ghahramani F. and Helemskii A.Y.A., “ The amenability of measure algebras”, J. London Math. Soc. (2) 66, pp. 213-226,         [ Links ](2002).
[D-H] Duncan J. and Houssainun S.A.R.,“ The second dual of a Banach algebra”, Proc. Roy. Soc. Edinburgh A 84, pp. 309-325,         [ Links ](1979).
[D-L] Dales H.G. and Lau A.T.-M.,“ The second duals of Beurling algebras”, Mem. Amer. Math. Soc. 177, No. 386,         [ Links ](2005).
[F-R] Forrest B. and Runde V.,“ Amenability and weak amenability of the Fourier algebra”, Math. Z. 250 4, pp. 731-744,         [ Links ](2005).
[G-L] Ghahramani F. and Laali J.“ Amenability and topological centers of the second duals of Banach algebras”, Bull. Austral. Math. Soc. 65, pp. 191-197,         [ Links ](2002).
[G-L-L] Ghahramani F., Lau A.T.M. and Losert V.,“ Isometric isomorphisms between Banach algebras related to locally compact groups”, Trans, Amer. Math. Soc. 321, pp. 273-383,         [ Links ](1990).
[G-L-W] Ghahramani F., Loy R.J. and Willis G.,“ Amenability and weak amenability of second conjugate Banach algebras”, Proc. Amer. Math. Soc. 124, pp. 1489-1497,         [ Links ](1996).
[Go] Gourdeau F.,“Amenability and the second dual of a Banach algebra“, Studia Math. 125, pp. 45-80,         [ Links ](1997).
[Gro] Gronback N.,“ Amenability of weighted convolution algebras on locally compact groups”, Trans. Amer. Math. Soc. 319, pp. 765-775,         [ Links ](1990).
[Gra] Granirer E.,“ Amenability and semisimplicity for second duals of quotients of the Fourier algebra A(G),”J.Austral. Math. Soc. (Series A) 63, pp. 289-296,         [ Links ](1997).
[L-L] Lau A.T.M and Loy R.J.,“ Weak amenability of Banach algebras on locally compact groups”, J. Funct. Anal. 145, pp. 175-204,         [ Links ](1997).
[P] Pym J.S.,“ Remarks on the second duals of Banach algebras”, Nigerian Math. Soc. 2, pp. 31-33,         [ Links ](1983).
[R1] Rejali A.,“ The analogue of weighted group algebra for semitopological semigroups”, J. Sci. I.R. Iran 6, pp. 113-120,         [ Links ](1995).
[R2] Rejali A.,“ Weighted function spaces on topological groups”, Bull. Iranian Math. Soc. 22, pp. 43-63,         [ Links ](1996).
[S] Sherman S.,“ The second adjoint of a C*-algebra,” Proc. Intern. Congr. Math. Cambridge, I, 470,         [ Links ](1950).
[U1] Ulger A.,“ Arens regularity of weakly sequentially complete Banach algebras”, Proc. Amer. Math. Soc. 127, pp. 3221-3227,         [ Links ](1999).
[U2] Ulger A.,“ Centeral elements of A** for certain Banach algebras A without bounded approximate identities,”Glasgow Math. J. 41, pp. 369-377,         [ Links ](1999).
[W] White M.,“ Characters on weighted amenable groups”, Bull. London Math. Soc. 23, pp. 375-380,         [ Links ](1991).
[Y1] Young N.,“ The irregularity of multiplication in group algebras,” Quart. J. Math. Oxford (2) 24, pp. 59-62,         [ Links ](1973).
[Y2] Young N.,“ Separate continuity and multilinear operations”, Proc. London Math. Soc. (3) 26, pp. 289-319,         [ Links ](1973).
[Y3] Young N.,“ Periodicity of functionals and representations of normed algebras on reflexive spaces,” Proc. Edinburgh Math. Soc. 20, pp. 100-120, (1976).
        [ Links ]

A. REJALI
Department of Mathematics
Isfahan University
Isfahan 81746-73441
Iran
Chile
e-mail : mailto:rejali@sci.ui.ac.ir

H. R. E. VISHKI
Faculty of Mathematical Sciences
Ferdowsi University, Mashhad
P.O. Box 91775-1159
Iran
e-mail : mailto:vishki@ferdowsi.um.ac.ir

Received : April 2007. Accepted : October 2007

 

Creative Commons License All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License