Mustafayev, H. S.2025-05-102025-05-1020060003-889X10.1007/s00013-006-1753-32-s2.0-33750992173https://doi.org/10.1007/s00013-006-1753-3https://hdl.handle.net/20.500.14720/6749Let A be a complex, commutative Banach algebra and let M-A be the structure space of A. Assume that there exists a continuous homomorphism h : L-1(G) -> A with dense range, where L-1(G) is the group algebra of a locally compact abelian group G. The main results of this paper can be summarized as follows: (a) If the dual space A* has the Radon-Nikodym property, then M-A is scattered (i.e., it has no nonempty perfect subset) and A* center dot A = (SPAN) over barM(A). (b) If the algebra A has an identity, then the space A* has the Radon-Nikodym property if and only if A* = (span) over bar M-A. Furthermore, any of these conditions implies that M-A is scattered. Several applications are given.eninfo:eu-repo/semantics/closedAccessArticle875Q3Q3449457WOS:000241947600009