Volterra-like Banach algebras and their second duals

This paper presents and studies a class of algebras which includes the usua l Volterra algebra. Roughly speaking, they relate to the Volterra algebra i n the way a general locally compact group relates to Fg. We show that they can be viewed as quotients of some semigroup algebras introduced by BAKER a nd BAKER [1]. Their sets of nilpotent elements are dense. We investigate th e 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 reta ined here.