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Ditkin's condition and primary ideals in central Beurling algebras

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Abstract

In this note some questions of ideal theory for the center and more generally theB-fixed subalgebras of a Beurling algebraL 1ω (G) are discussed. Sufficient conditions on ω are given for these subagebras to satisfy Ditkin's condition, or for primary ideals to be maximal or at least of finite codimension.

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References

  1. Domar, Y.: Harmonic analysis based on certain commutative Banach algebras. Acta Math.96, 1–66 (1956).

    Google Scholar 

  2. Gelfand, I., D. Raikov, andG. Shilov: Commutative Normed Rings. New York: Chelsea. 1964.

    Google Scholar 

  3. Grosser, S., andM. Moskowitz: Compactness conditions in topological groups. J. reine Angew. Math.246, 1–40 (1971).

    Google Scholar 

  4. Hulanicki, A., J. Jenkins, H. Leptin, andT. Pytlik: Remarks on Wiener's Tauberian theorems for groups with polynomial growth. Coll. Math.35, 293–304 (1976).

    Google Scholar 

  5. Liukkonen, J., andR. Mosak: Harmonic analysis and centers of Beurling algebras. Comm. Math. Helv. (To appear.)

  6. Liukkonen, J., andR. Mosak: Harmonic analysis and centers of group algebras. Trans. Amer. Math. Soc.195, 147–163 (1947).

    Google Scholar 

  7. Mosak, R.: TheL 1-andC *-algebras of [FIA] B groups, and their representations. Trans. Amer. Math. Soc.163, 277–310 (1972).

    Google Scholar 

  8. Reiter, H.: Classical Harmonic Analysis and Locally Compact Groups. Oxford: Oxford University Press. 1968.

    Google Scholar 

  9. Rickart, C.: General Theory of Banach Algebras. Princeton: Van Nostrand. 1960.

    Google Scholar 

  10. Spector, R.: Groupes localement isomorphes et transformation de Fourier avec poids. Ann. Inst. Fourier, Grenoble19, 195–217 (1969).

    Google Scholar 

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Research partially supported by the National Science Foundation.

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Mosak, R.D. Ditkin's condition and primary ideals in central Beurling algebras. Monatshefte für Mathematik 85, 115–124 (1978). https://doi.org/10.1007/BF01297541

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