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 (SCI-Expanded) identifier identifier


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.