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Fréchet algebras with a Laurent series generator and the annulus algebras

  • S. J. Bhatt (a1), H. V. Dedania (a1) and S. R. Patel (a1)

Abstract

Banach and Fréchet algebras with a Laurent series generator are investigated leading, via the discrete Beurling algebras, to functional analytic characterisations of the holomorphic function algebras on the annulus as well as the C-algebra on the unit circle.

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References

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[1]Carpenter, R.L., ‘Uniqueness of topology for commutative semisimple F-algebras’, Proc. Amer. Math. Soc. (1971), 113117.
[2]Gelfand, I., Raikov, D. and Shilov, G., Commutative normed rings (Chelsea Publ. Co., Bronx, NY, 1964).
[3]Goldmann, H., Uniform Fréchet algebras, North Holland Mathematics Studies 162 (North Holland Publ. Co., Amsterdam, 1990).
[4]Loy, R.J., ‘Banach algebras of power series’, J. Austral. Math. Soc. 17 (1974), 263273.
[5]Wang, D. and Watson, S., ‘A characterization of the algebra of holomorphic functions on a simply connected domain’, Internat. J. Math. Sci. 12 (1989), 6568.
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