Arens regularity and the 𝐴_{𝑝}(𝐺) algebras

Forrest, Brian

doi:10.1090/S0002-9939-1993-1169026-3

Arens regularity and the $A\sb p(G)$ algebras

Author: Brian Forrest
Journal: Proc. Amer. Math. Soc. 119 (1993), 595-598
MSC: Primary 43A15
DOI: https://doi.org/10.1090/S0002-9939-1993-1169026-3
MathSciNet review: 1169026
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a locally compact group. Let ${A_p}(G)$ denote the Herz algebra associated with $1 < p < \infty$ . We show that, for a large class of groups which contains every commutative group, ${A_p}(G)$ is Arens regular if and only if is finite.

[1] R. E. Edwards and G. I. Gaudry, Littlewood-Paley and multiplier theory, Springer-Verlag, Berlin-New York, 1977. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 90. MR 0618663
[2] Pierre Eymard, L’algèbre de Fourier d’un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181–236 (French). MR 228628
[3] Brian Forrest, Arens regularity and discrete groups, Pacific J. Math. 151 (1991), no. 2, 217–227. MR 1132386
[4] E. E. Granirer, On convolution operators which are far from being convolution by a bounded measure (to appear).
[5] Carl Herz, Harmonic synthesis for subgroups, Ann. Inst. Fourier (Grenoble) 23 (1973), no. 3, 91–123 (English, with French summary). MR 355482
[6] Otto H. Kegel and Bertram A. F. Wehrfritz, Locally finite groups, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1973. North-Holland Mathematical Library, Vol. 3. MR 0470081
[7] Anthony To Ming Lau and Ali Ülger, Some geometric properties on the Fourier and Fourier-Stieltjes algebras of locally compact groups, Arens regularity and related problems, Trans. Amer. Math. Soc. 337 (1993), no. 1, 321–359. MR 1147402, https://doi.org/10.1090/S0002-9947-1993-1147402-7
[8] Anthony To Ming Lau and James C. S. Wong, Weakly almost periodic elements in 𝐿_{∞}(𝐺) of a locally compact group, Proc. Amer. Math. Soc. 107 (1989), no. 4, 1031–1036. MR 991701, https://doi.org/10.1090/S0002-9939-1989-0991701-0
[9] Alan L. T. Paterson, Amenability, Mathematical Surveys and Monographs, vol. 29, American Mathematical Society, Providence, RI, 1988. MR 961261