Let be a weight function on a locally compact group and let be the subspace of consisting of all functionals that vanish at infinity. We first introduce an Arens product on under which it is a Banach algebra. We then show that the existence of a nonzero compact right multiplier on is equivalent to compactness of . We also prove that if is Arens regular, then is discrete.
Mohammad Javad Mehdipour. Gholam Reza Moghimi. "THE EXISTENCE OF NONZERO COMPACT RIGHT MULTIPLIERS AND ARENS REGULARITY OF WEIGHTED BANACH ALGEBRAS." Rocky Mountain J. Math. 52 (6) 2101 - 2112, December 2022. https://doi.org/10.1216/rmj.2022.52.2101