Duals and topological center of a class of matrix algebras with applications

Author:
G. H. Esslamzadeh

Journal:
Proc. Amer. Math. Soc. **128** (2000), 3493-3503

MSC (2000):
Primary 43A20, 46H05

Published electronically:
May 18, 2000

MathSciNet review:
1694860

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Abstract | References | Similar Articles | Additional Information

Abstract: We characterize the topological center of a class of matrix algebras, which are called -Munn algebras. This involves a characterization of Arens regular semigroup algebras for a large class of semigroups, which is an extension of Young's Theorem for semigroups. We show by some counter examples that only up to a certain extent Young's Theorem can be generalized.

**1.**Richard Arens,*Operations induced in function classes*, Monatsh. Math.**55**(1951), 1–19. MR**0044109****2.**Frank F. Bonsall and John Duncan,*Complete normed algebras*, Springer-Verlag, New York-Heidelberg, 1973. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 80. MR**0423029****3.**Paul Civin and Bertram Yood,*The second conjugate space of a Banach algebra as an algebra*, Pacific J. Math.**11**(1961), 847–870. MR**0143056****4.**A. H. Clifford and G. B. Preston,*The algebraic theory of semigroups. Vol. I*, Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1961. MR**0132791****5.**G. H. Esslamzadeh,*Banach algebra structure and amenability of a class of matrix algebras with applications*, Ph.D. Thesis, University of Alberta, 1998.**6.**G. H. Esslamzadeh,*Banach algebra structure and amenability of a class of matrix algebras with applications*, J. Funct. Anal.**161**(1999), 364-383. CMP**99:09****7.**G. H. Esslamzadeh,*Representation theory and positive functionals of involutive**Munn algebras*, in preparation.**8.**F. Ghahramani and A. T. Lau,*Isometric isomorphisms between the second conjugate algebras of group algebras*, Bull. London Math. Soc.**20**(1988), no. 4, 342–344. MR**940290**, 10.1112/blms/20.4.342**9.**F. Ghahramani, A. T. Lau, and V. Losert,*Isometric isomorphisms between Banach algebras related to locally compact groups*, Trans. Amer. Math. Soc.**321**(1990), no. 1, 273–283. MR**1005079**, 10.1090/S0002-9947-1990-1005079-2**10.**Edwin Hewitt and Kenneth A. Ross,*Abstract harmonic analysis. Vol. I: Structure of topological groups. Integration theory, group representations*, Die Grundlehren der mathematischen Wissenschaften, Bd. 115, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. MR**0156915****11.**J. M. Howie,*An introduction to semigroup theory*, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1976. L.M.S. Monographs, No. 7. MR**0466355****12.**Nilgün Işık, John Pym, and Ali Ülger,*The second dual of the group algebra of a compact group*, J. London Math. Soc. (2)**35**(1987), no. 1, 135–148. MR**871771**, 10.1112/jlms/s2-35.1.135**13.**Anthony To Ming Lau,*The second conjugate algebra of the Fourier algebra of a locally compact group*, Trans. Amer. Math. Soc.**267**(1981), no. 1, 53–63. MR**621972**, 10.1090/S0002-9947-1981-0621972-9**14.**Anthony To Ming Lau and Viktor Losert,*On the second conjugate algebra of 𝐿₁(𝐺) of a locally compact group*, J. London Math. Soc. (2)**37**(1988), no. 3, 464–470. MR**939122**, 10.1112/jlms/s2-37.3.464**15.**Anthony To Ming Lau and Ali Ülger,*Topological centers of certain dual algebras*, Trans. Amer. Math. Soc.**348**(1996), no. 3, 1191–1212. MR**1322952**, 10.1090/S0002-9947-96-01499-7**16.**W. D. Munn,*On semigroup algebras*, Proc. Cambridge Philos. Soc.**51**(1955), 1–15. MR**0066355****17.**Theodore W. Palmer,*Banach algebras and the general theory of *-algebras. Vol. I*, Encyclopedia of Mathematics and its Applications, vol. 49, Cambridge University Press, Cambridge, 1994. Algebras and Banach algebras. MR**1270014****18.**W. Rudin,*Functional Analysis*, Tata McGraw Hill, New Delhi, 1989.**19.**N. J. Young,*The irregularity of multiplication in group algebras*, Quart J. Math. Oxford Ser. (2)**24**(1973), 59–62. MR**0320756**

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Additional Information

**G. H. Esslamzadeh**

Affiliation:
Faculty of Mathematics and Computer Science, Tehran Polytechnic University, 424 Hafez Avenue, 15914 Tehran, Iran

Email:
hesslam@cic.aku.ac.ir

DOI:
https://doi.org/10.1090/S0002-9939-00-05521-0

Received by editor(s):
January 22, 1999

Published electronically:
May 18, 2000

Additional Notes:
This work was supported by a scholarship from MCHE, Iran, and also partially by the Department of Mathematical Sciences, University of Alberta. The author thanks both of these agencies for their kind support.

Communicated by:
Dale Alspach

Article copyright:
© Copyright 2000
American Mathematical Society