Volterra-like Banach Algebras and their Second Duals

 This paper presents and studies a class of algebras which includes the usual Volterra algebra. Roughly speaking, they relate to the Volterra algebra in the way a general locally compact group relates to ℝ. We show that they can be viewed as quotients of some semigroup algebras introduced by Baker and Baker 1]. Their sets of nilpotent elements are dense. We investigate the second duals of these algebras and find that most of the properties found in 7] for the biduals of the group algebras L ¹(G) for compact G are retained here. Received 8 July 1997; in revised form 17 November 1997