In a previous paper (Arens; these references are to the bibliography of the present paper) there was investigated (in a more general, abstract setting) the process of forming the adjoint operation m*\ Z-XX^Ydefined, for fEZ~, xEX, by TM*(f, x)(y) = f(m(x, y)) (y £ F). The simple proof that m* satisfies 1.1, 1.2, and 1.3 with the same value of M is given in (Arens). This construction can be iter...

Let $mathcal{A}$ be a Banach algebra with BAI and $E$ be an introverted subspace of $mathcal{A}^prime$. In this paper we study the quotient Arens regularity of $mathcal{A}$ with respect to $E$ and prove that the group algebra $L^1(G)$ for a locally compact group $G$, is quotient Arens regular with respect to certain introverted subspace $E$ of $L^infty(G)$. Some related result are given as well.

‎We present a characterization of Arens regular semigroup algebras‎ ‎$ell^1(S)$‎, ‎for a large class of semigroups‎. ‎Mainly‎, ‎we show that‎ ‎if the set of idempotents of an inverse semigroup $S$ is finite‎, ‎then $ell^1(S)$ is Arens regular if and only if $S$ is finite‎.

Cannibalism as a topic of interest, both general and anthropological, has seen a revival of concern in the last seven years or so. Primarily responsible for this revival is the controversial stance taken by William Arens in his book, The ManEating Myth: Anthropology and Anthropophagy (1979). Following the publication of this work has been a deluge of articles and books, popular and specialized,...

and similarly for the right topological centre Z(r)(A′′). The algebra A is said to be Arens regular if Z(`)(A′′) = Z(r)(A′′) = A′′ and strongly Arens irregular if Z(`)(A′′) = Z(r)(A′′) = A. For example, every C∗-algebra is Arens regular [2]. There has been a great deal of study of these two algebras, especially in the case where A is the group algebra L(G) for a locally compact group G. Results...