On the radical for some class of Banach algebras

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Mustafaev G. S.

FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, vol.41, no.3, pp.241-244, 2007 (SCI-Expanded)

• 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 (SCI-EXPANDED), Scopus
• Page Numbers: pp.241-244
• Van Yüzüncü Yıl University Affiliated: Yes

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.