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

HTML articles powered by AMS MathViewer

- 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 ${M_\phi }$.## References

- Frank F. Bonsall and John Duncan,
*Complete normed algebras*, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 80, Springer-Verlag, New York-Heidelberg, 1973. MR**0423029** - Andrew Browder,
*Introduction to function algebras*, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR**0246125** - P. G. Dixon,
*Factorization and unbounded approximate identities in Banach algebras*, Math. Proc. Cambridge Philos. Soc.**107**(1990), no. 3, 557–571. MR**1041485**, DOI 10.1017/S030500410006881X - Robert S. Doran and Josef Wichmann,
*Approximate identities and factorization in Banach modules*, Lecture Notes in Mathematics, vol. 768, Springer-Verlag, Berlin-New York, 1979. MR**555240** - Theodore W. Gamelin,
*Uniform algebras*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1969. MR**0410387** - John B. Garnett,
*Bounded analytic functions*, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR**628971** - Kenneth Hoffman,
*Banach spaces of analytic functions*, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR**0133008** - Kenneth Hoffman,
*Bounded analytic functions and Gleason parts*, Ann. of Math. (2)**86**(1967), 74–111. MR**215102**, DOI 10.2307/1970361 - Edgar Lee Stout,
*The theory of uniform algebras*, Bogden & Quigley, Inc., Publishers, Tarrytown-on-Hudson, N.Y., 1971. MR**0423083**
G. A. Willis,

*Examples of factorization without bounded approximate units*, preprint, Research Report no. 12, 1989, Mathematical Centre, Australian National University, Canberra.

## Additional Information

- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**113**(1991), 435-441 - MSC: Primary 46J15
- DOI: https://doi.org/10.1090/S0002-9939-1991-1055776-4
- MathSciNet review: 1055776