Geodesic
On the Radical for Some Class of Banach Algebras
Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 3, pp. 89-93

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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, spectrum.
Mots-clés : homomorphism 
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     author = {H. S. Mustafaev},
     title = {On the {Radical} for {Some} {Class} of {Banach} {Algebras}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2007_41_3_a6/}
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H. S. Mustafaev. On the Radical for Some Class of Banach Algebras. Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 3, pp. 89-93. http://geodesic.mathdoc.fr/item/FAA_2007_41_3_a6/