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.
Similar content being viewed by others
References
Domar, Y.: Harmonic analysis based on certain commutative Banach algebras. Acta Math.96, 1–66 (1956).
Gelfand, I., D. Raikov, andG. Shilov: Commutative Normed Rings. New York: Chelsea. 1964.
Grosser, S., andM. Moskowitz: Compactness conditions in topological groups. J. reine Angew. Math.246, 1–40 (1971).
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).
Liukkonen, J., andR. Mosak: Harmonic analysis and centers of Beurling algebras. Comm. Math. Helv. (To appear.)
Liukkonen, J., andR. Mosak: Harmonic analysis and centers of group algebras. Trans. Amer. Math. Soc.195, 147–163 (1947).
Mosak, R.: TheL 1-andC *-algebras of [FIA] − B groups, and their representations. Trans. Amer. Math. Soc.163, 277–310 (1972).
Reiter, H.: Classical Harmonic Analysis and Locally Compact Groups. Oxford: Oxford University Press. 1968.
Rickart, C.: General Theory of Banach Algebras. Princeton: Van Nostrand. 1960.
Spector, R.: Groupes localement isomorphes et transformation de Fourier avec poids. Ann. Inst. Fourier, Grenoble19, 195–217 (1969).
Author information
Authors and Affiliations
Additional information
Research partially supported by the National Science Foundation.
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01297541