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Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)

     

Topological centers of certain dual algebras

Author(s): Anthony To-Ming Lau; Ali Ülger
Journal: Trans. Amer. Math. Soc. 348 (1996), 1191-1212.
MSC (1991): Primary 43A20; Secondary 46H05
MathSciNet review: 1322952
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Abstract: Let $A$ be a Banach algebra with a bounded approximate identity. Let $Z_1$ and $\widetilde Z_2$ be, respectively, the topological centers of the algebras $A^{**}$ and $(A^*A)^*$. In this paper, for weakly sequentially complete Banach algebras, in particular for the group and Fourier algebras $L^1(G)$ and $A(G)$, we study the sets $Z_1$, $\widetilde Z_2$, the relations between them and with several other subspaces of $A^{**}$ or $A^*$.

References:

[1]
Arens, R., The adjoint of a bilinear operation, Proc. Amer. Math. Soc. 2 (1951), 839-848. MR 13:659f

[2]
Bonsall, F.F. and Duncan, J., Complete Normed Algebras, Springer-Verlag, Berlin, 1973. MR 54:11013

[3]
Cecchini, C. and Zappa, A., Some results on the center of an algebra of operators on $VN(G)$ for the Heisenberg group, Canad. J. Math. 33 (1981), 1469-1486 MR 83f:22003

[4]
Cigler, J., Losert, V. and Michor, P., Banach modules and functors on categories of Banach spaces, Lecture Notes in Pure and Appl. Math., 46, Marcel Dekker, 1979. MR 80j:46112

[5]
Derighetti, A., Some results on the Fourier-Stieltjes algebra of a locally compact group, Comm. Math. Helv. 45 (1970), 219-228. MR 54:856

[6]
Diestel, J. and Uhl, J.J., Jr., Vector measures, Math. Surveys, Vol. 15, Amer. Math. Soc., Providence, RI, 1977. MR 56:12216

[7]
Eymard, P., L'algèbre de Fourier d'un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181-236. MR 37:4208

[8]
Ghahramani, F. and McClure, J. P., Module homomorphisms of the dual modules of convolution Banach algebras, Canad. Math. Bull. (2) 35 (1992), 180-185. MR 93f:43004

[9]
Ghahramani, F., Lau, A.T., and Losert, V., Isometric isomorphisms between Banach algebra related to locally compact groups, Trans. Amer. Math. Soc. 321 (1990), 273-283. MR 90m:43010

[10]
Godefroy, G., Existence and uniqueness of isomorphic preduals: a survey, Contemporary Math. 85 (1989), 131-193. MR 90b:46035

[11]
Granirer, E., Exposed points of convex sets and weak sequential convergence, Mem. Amer. Math. Soc., No. 123 (1972). MR 51:1343

[12]
Granirer, E. and Leinert, M., On some topologies which coincide on the unit sphere of the Fourier-Stieltjes algebra $B(G)$ and the measure algebra $M(G)$, Rocky Mountain J. Math. 11 (1981), 459-472. MR 85f:43009

[13]
Grosser, M., Arens semi-regular Banach algebras, Monatsh. Math. 98 (1984), 41-52. MR 86d:46042

[14]
Grosser, M. and Losert, V., The norm-strict bidual of a Banach algebra and the dual of $C_u(G)$, Manuscripta Math. 45 (1984), 127-46. MR 86b:46073

[15]
Grothendieck, A., Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc., No. 16 (1955). MR 17:877d

[16]
Grothendieck, A., Critères de compacité dans les espaces functionels généraux, Amer. J. Math. 74 (1975), 168-186. MR 13:857e

[17]
Hewitt, E. and Ross, K., Abstract Harmonic Analysis, Vols. I and II, New York, 1970. MR 41:7378

[18]
Isik, N., Pym, J.S. and Ülger, A., The second dual of the group algebra of a compact group, J. London Math. Soc. (2) 35 (1987), 135-148. MR 88f:43012

[19]
Lau, A.T., Uniformly continuous functionals of the Fourier algebra of any locally compact group, Trans. Amer. Math. Soc. 251 (1979), 39-59. MR 80m:43009

[20]
Lau, A.T., Continuity of Arens multiplication on the dual space of bounded uniformly continuous functions on locally compact groups and topological semigroups, Math. Proc. Camb. Philos. Soc. 99 (1986), 273-283. MR 87i:43001

[21]
Lau, A.T. and Losert, V., On the second conjugate algebra of a locally compact group, J. London Math. Soc. 37 (1988), 464-470. MR 89e:43007

[22]
Lau, A.T. and Losert, V., The $C^*\text{-algebra}$ generated by operators with compact support on a locally compact group, Journal of Functional Analysis 112 (1993), 1-30. MR 94d:22005

[23]
Leptin, H., Sur l'algèbre de Fourier d'un group localement compact, C.R. Acad. Sci. Paris Sér. A-B 266 (1968), 1180-1182. MR 39:362

[24]
McWilliams, R.D., A note on weak sequential convergence, Pacific J. Math. 12 (1962), 333-335. MR 26:6724

[25]
Parsons, D.J., The center of the second dual of a commutative semigroup algebra, Math. Proc. Camb. Phil. Soc. 95 (1984), 71-92. MR 85c:43004

[26]
Pym, J.S., The convolution of functionals on spaces of bounded functions, Proc. London Math. Soc. 15 (1965), 84-104. MR 30:3367

[27]
Ülger, A., Arens regularity sometimes implies the RNP, Pacific J. Math. 143 (1990), 377-399. MR 92d:46127

[28]
Wendel, J.G., Left centralizers and isomorphisms of group algebras, Pacific J. Math. 2 (1952), 251-261. MR 14:262c

[29]
Zappa, A., The center of the convolution algebra $C_u(G)$, Rend. Sem. Math. Univ. Padova 52 (1974), 71--84. MR 53:14014

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Additional Information:

Anthony To-Ming Lau
Affiliation: Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: tlau@vega.math.ualberta.ca

Ali Ülger
Affiliation: Department of Mathematics, Bo\={g}azici University, 80815 Bebek-Istanbul, Turkey
Email: ulger@boun.edu.tr

DOI: 10.1090/S0002-9947-96-01499-7
PII: S 0002-9947(96)01499-7
Keywords: Topological center, multiplier algebra, group algebra and Fourier algebra
Received by editor(s): September 4, 1994
Received by editor(s) in revised form: March 27, 1995
Additional Notes: The research of the first author is supported by an NSERC grant.
The research of the second author is supported by TUBA
Copyright of article: Copyright 1996, American Mathematical Society




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