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Proceedings of the American Mathematical Society

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Compact endomorphisms and closed ideals in Banach algebras

Author: Sandy Grabiner
Journal: Proc. Amer. Math. Soc. 92 (1984), 547-548
MSC: Primary 46H05; Secondary 46J05, 47A15
MathSciNet review: 760943
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Abstract: Every infinite-dimensional Banach algebra with a nonzero compact endomorphism has a proper closed nonzero two-sided ideal. When the algebra is commutative, the ideal is also an ideal in the multiplier algebra.

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