On the radical for some class of Banach algebras


Mustafaev G. S.

FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, vol.41, no.3, pp.241-244, 2007 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 3
  • Publication Date: 2007
  • Doi Number: 10.1007/s10688-007-0021-z
  • Journal Name: FUNCTIONAL ANALYSIS AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.241-244

Abstract

Let A be a complex Banach algebra. It is well known that the second dual A** of A can be equipped with a multiplication that extends the original multiplication on A and makes A** a Banach algebra. We show that Rad(A) (perpendicular to)(A* . A) and Rad(A**) = (A* . A)(perpendicular to) for some classes of Banach algebras A with scattered structure space. Some applications of these results are given.