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

  1. 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.

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