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Bipositive Isomorphisms Between Beurling Algebras and Between their Second Dual Algebras

Published online by Cambridge University Press:  20 November 2018

F. Ghahramani  and
S. Zadeh
F. Ghahramani
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, MB R3T 2N2 e-mail: fereidou@cc.umanitoba.ca
S. Zadeh
Affiliation:
Laboratoire de Mathématiques, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cedex e-mail: jsafoora@gmail.com
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Abstract

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Let $G$ be a locally compact group and let $\omega$ be a continuous weight on $G$. We show that for each of the Banach algebras ${{L}^{1}}\left( G,\,\omega \right),\,M\left( G,\,\omega \right),\,LUC{{\left( G,\,{{\omega }^{-1}} \right)}^{*}}$, and ${{L}^{1}}{{\left( G,\,\omega \right)}^{**}}$, the order structure combined with the algebra structure determines the weighted group.

Keywords

43A2043A22locally compact groupBeurling algebraArens producttopological group isomorphismbipositive algebra isomorphism
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 69 , Issue 1 , 01 February 2017 , pp. 3 - 20
Copyright
Copyright © Canadian Mathematical Society 2017

References

[AB85] Aliprantis, C. D. and Burkinshaw, O., Positive operators. Pure and Applied Mathematics, 119, Academic Press, Inc., Orlando, FL, 1985.Google Scholar
[BD73] Bonsall, E.F. and J. Duncan, , Complete normed algebras. Ergebnisse der Mathematik undihrer Grenzgebiete, 80, Springer-Verlag, New York-Heidelberg, 1973.Google Scholar
[DL05] Dales, H. G. and Lau, A. T.-M., The second duals of Beurling algebras. Mem. Amer. Math. Soc. 177(2005), no. 836.http://dx.doi.Org/10.1090/memo/0836 Google Scholar
[Far98] Farhadi, H.-R., Bipositive isomorphisms between the second duals of group algebras of locally compact groups. Math. Proc. Cambridge Philos. Soc. 123(1998), no. 1, 95–99. http://dx.doi.Org/10.1017/S0305004197002065 Google Scholar
[Gha84] Ghahramani, E., Weighted group algebra as an ideal in its second dual space. Proc. Amer. Math. Soc. 90(1984), no. 1, 71–76. http://dx.doi.Org/10.1090/S0002-9939-1984-0722417-9 Google Scholar
[GL88] E.Ghahramani, and Lau, A. T., Isometric isomorphisms between the second conjugate algebras of group algebras. Bull. London Math. Soc. 20(1988), no. 4, 342–344.http://dx.doi.Org/10.1112/blms/20.4.342 Google Scholar
[GLL90] E.Ghahramani, , Lau, A. T., and V.|Losert, Isometric isomorphisms between Banach algebras related to locally compact groups. Trans. Amer. Math. Soc. 321(1990), no. 1, 273–283. http://dx.doi.org/10.1090/S0002-9947-1990-1005079-2 Google Scholar
[Gre65] Greenleaf, E.P., Norm decreasing homomorphisms of group algebras. Pacific J. Math. 15(1965), 1187–1219. http://dx.doi.org/10.2140/pjm.1965.15.1187 Google Scholar
[Gr09O] Grønbask, N., Amenability of weighted convolution algebras on locally compact groups. Trans. Amer. Math. Soc. 319(1990), no. 2, 765–775. http://dx.doi.org/10.1090/S0002-9947-1990-0962282-5 Google Scholar
[HR] Hewitt, E. and Ross, K. A., Abstract harmonic analysis. Vol. I. Structure of topological groups, integration theory, group representations. Second éd., Grundlehren der Mathematischen Wissenschaften, 115, Springer-Verlag, Berlin-New York, 1979.Google Scholar
[Joh64] Johnson, B. E., An introduction to the theory of centralizers. Proc. London Math. Soc. (3) 14(1964), 299–320. http://dx.doi.Org/10.1112/plms/s3-14.2.299 Google Scholar
[KanO9] Kaniuth, E., A course in commutative Banach algebras. Graduate Texts in Mathematics, 246, Springer, New York, 2009. http://dx.doi.Org/10.1007/978-0-387-72476-8 Google Scholar
[Kaw48] Kawada, Y., On the group ring of a topological group. Math. Japonicae 1(1948), 1–5. Google Scholar
[LM80] Lau, A. T. M. and McKennon, K., Isomorphisms of locally compact groups and Banach algebras. Proc. Amer. Math. Soc. 79(1980), 55–58. http://dx.doi.org/10.1090/S0002-9939-1980-0560583-5 Google Scholar
[Pal94] Palmer, T. W., Banach algebras and the general theory of *?-algebras. Cambridge University Press, Cambridge, 1994.Google Scholar
[Rud62] Rudin, W., Fourier analysis on groups. Interscience Tracts in Pure and Applied Mathematics, 12, Interscience Publishers, New York-London, 1962.Google Scholar
[Wen51] Wendel, J. G, On isometric isomorphism of group algebras. Pacific J. Math. 1(1951), 305–311. http://dx.doi.org/10.2140/pjm.1951.1305 Google Scholar