|
Duals and topological center of a class of matrix algebras with applications
Author(s):
G.
H.
Esslamzadeh
Journal:
Proc. Amer. Math. Soc.
128
(2000),
3493-3503.
MSC (2000):
Primary 43A20, 46H05
Posted:
May 18, 2000
Retrieve article in:
PDF
This article is available free of charge
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.
References:
-
- 1.
- R. Arens, Operations induced in function classes, Monatsh Math. 55 (1951), 1-19. MR 13:372b
- 2.
- F. F. Bonsall and J. Duncan, Complete normed algebras, Springer Verlag, Berlin, 1973. MR 54:11013
- 3.
- P. Civin and B. Yood, The second conjugate space of a Banach algebra, Pacific J. Math. 11 (1961), 847-870. MR 26:622
- 4.
- A. H. Clifford and J. B. Preston, The algebraic theory of semigroups I, Amer. Math. Soc. Surveys 7, 1961. MR 24:A2627
- 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. M. Lau, Isometric isomorphisms between the second conjugate algebras of group algebras, Bull. London Math. Soc. (4)20 (1988), 342-344. MR 89e:43008
- 9.
- F. Ghahramani, A.T. M. Lau and V. Losert, Isometric isomorphisms between Banach algebras related to locally compact groups, Trans. Amer. Math. Soc. 321 (1990), 273-283. MR 90m:43010
- 10.
- E. Hewitt and K. A. Ross, Abstract harmonic analysis I, Springer-Verlag, Berlin, 1987. MR 28:158
- 11.
- J. M. Howie, An introduction to semigroup theory, Academic Press, London, 1976. MR 57:6235
- 12.
- N. Isik, J. Pym and A. Ulger, The second dual of the group algebra of a compact group, J. London Math. Soc. (2)35 (1987), 135-148. MR 88f:43012
- 13.
- A. T. M. Lau, The second conjugate algebra of the Fourier algebra of a locally compact group, Trans. Amer. Math. Soc. 267 (1981), 53-63. MR 83e:43009
- 14.
- A. T. M. Lau and V. Losert, On the second conjugate algebra of the group algebra of a locally compact group, J. London Math. Soc. 37 (1988), 464-470. MR 89e:43007
- 15.
- A. T. M. Lau and A. Ulger, Topological centers of certain dual algebras, Trans. Amer. Math. Soc. (3)348 (1996), 1191-1212. MR 96h:43003
- 16.
- W. D. Munn, On semigroup algebras, Proc. Cambridge Phil. Soc. 51 (1955), 1-15. MR 16:561c
- 17.
- T. Palmer, Banach algebras and the general theory of *-algebras, Vol. I, Cambridge University Press, 1994. MR 95c:46002
- 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 (2)24 (1973), 59-62. MR 47:9290
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
43A20, 46H05
Retrieve articles in all Journals with MSC
(2000):
43A20, 46H05
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:
10.1090/S0002-9939-00-05521-0
PII:
S 0002-9939(00)05521-0
Received by editor(s):
January 22, 1999
Posted:
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
Copyright of article:
Copyright
2000,
American Mathematical Society
|