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Funktsional. Anal. i Prilozhen., 2007, Volume 41, Issue 3, Pages 89–93 (Mi faa2870)  

Brief communications

On the Radical for Some Class of Banach Algebras

H. S. Mustafaev

Yuzuncu Yil University

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 $\operatorname{Rad}(A)= ^\bot(A^*\cdot A)$ and $\operatorname{Rad}(A^{**})=(A^*\cdot A)^\bot$ for some classes of Banach algebras $A$ with scattered structure space. Some applications of these results are given.

Keywords: Banach algebra, group algebra, radical, homomorphism, spectrum

DOI: https://doi.org/10.4213/faa2870

Full text: PDF file (168 kB)
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English version:
Functional Analysis and Its Applications, 2007, 41:3, 241–244

Bibliographic databases:

UDC: 517.98
Received: 28.06.2005

Citation: H. S. Mustafaev, “On the Radical for Some Class of Banach Algebras”, Funktsional. Anal. i Prilozhen., 41:3 (2007), 89–93; Funct. Anal. Appl., 41:3 (2007), 241–244

Citation in format AMSBIB
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