TY - JOUR ID - 171452 TI - Arens regularity of ideals in $A(G)$, $A_{cb}(G)$ and $A_M(G)$. JO - Journal of the Iranian Mathematical Society JA - JIMS LA - en SN - AU - Forrest, B. AU - Sawatzky, J. AU - Thamizhazhagan, A. AD - Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1. Y1 - 2023 PY - 2023 VL - 4 IS - 1 SP - 5 EP - 25 KW - Fourier algebra KW - multipliers KW - Arens regularity KW - uniformly continuous functionals KW - topologically invariant means DO - 10.30504/jims.2023.385500.1091 N2 - In this paper, we look at the question of when various ideals in the Fourier algebra $A(G)$ or its closures $A_M(G)$ and $A_{cb}(G)$ in, respectively, its multiplier and $cb$-multiplier algebra are Arens regular. We show that in each case, if a non-zero ideal is Arens regular, then the underlying group $G$ must be discrete. In addition, we show that if an ideal $I$ in $A(G)$ has a bounded approximate identity, then it is Arens regular if and only if it is finite-dimensional. UR - https://jims.ims.ir/article_171452.html L1 - https://jims.ims.ir/article_171452_757f30a2988d0c0f2d7430947e4be2f2.pdf ER -