A commutative Banach algebra with factorization of elements but not of pairs

Ouzomgi, S. I.

doi:10.1090/S0002-9939-1991-1055776-4

A commutative Banach algebra with factorization of elements but not of pairs
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by S. I. Ouzomgi PDF

Proc. Amer. Math. Soc. 113 (1991), 435-441 Request permission

Abstract:

We find a one-point Gleason part $\phi$ off the Šilov boundary of ${H^\infty }(\Delta )$ such that the maximal ideal ${M_\phi }$ factors but such that pairs do not factor in ${M_\phi }$.

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Examples of factorization without bounded approximate units