Radicals and Homomorphic Images of $C^*$-Algebras
Commun. Korean Math. Soc. 1999 Vol. 14, No. 2, 365-371
Hyuk Han
Seonam University
Abstract : In this paper, we prove that the range of homomorphism from a C*-algebra $A$ into a commutative Banach algebra $B$ whose radical is nil contains no non-zero element of the radical of $B$. Using this result we show that there is no non-zero homomorphism from a C*-algebra into a commutative radical nil Banach algebra.
Keywords : homomorphism, radical, quasi-nilpotent
MSC numbers : 46H40, 46J45
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