# On the intersection of the principal ideals generated by powers in a Banach Algebra

by P.G.Dixon

*Radical Banach algebras and automatic continuity (Long Beach, Calif., 1981),* 340-341,
Lecture Notes in Math., **975**, (Springer, Berlin-New York, 1983).

1991 Mathematics Subject Classification: 46H10

## Abstract

The following question was raised by J. C. Tripp in the preceding paper in these proceedings
[**1**]:

if *b* is an element of a Banach algebra *B* such that the intersection of all the
principal ideals *b^n B* is trivial, is the intersection of their closures trivial? We give an
example to show that the answer is negative, even if *B* is commutative and separable.

### Reference

- J. C. Tripp, `Automatic continuity of homomorphisms into Banach algebras',
*Radical Banach algebras and automatic continuity (Long Beach, Calif., 1981),* 334-339,
Lecture Notes in Math., **975**, (Springer, Berlin-New York, 1983).
(1987), 213-216.

## Availability

No reprints of the paper are available.

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