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manuscripta mathematica

, Volume 43, Issue 1, pp 85–86 | Cite as

P-commutativity of the Banach algebra L1**(G)

  • R. S. Doran
  • Wayne Tiller
Article

Abstract

Let G be a compact abelian group. It is known that the second conjugate space L1**(G) of the group algebra L1(G) is a noneommutative, nonsemisimple, Banach algebra. It is not known if L1**(G) admits an involution. If it does, we show that it is P-coimnutative, and hence enjoys many of the properties of commutative Banach algebras.

Keywords

Abelian Group Number Theory Algebraic Geometry Topological Group Banach Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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    CIVIN, P., YOOD, B.: The second conjugate space of a Banach algebra as an algebra, Pacific J. Math. 11, 847–870 (1961)Google Scholar
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    DORAN, R. S., WICHMANN, J.: Approximate identities and factorization in Banach modules. Lecture Notes in Math.768, 305 pp., Berlin-Heidelberg-New York: Springer 1979Google Scholar
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    RICKART, C. E.: General theory of Banach algebras, Princeton: D. Van Nostrand 1960Google Scholar
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    TILLER, W.: P-commutative Banach *-algebras. Trans. Amer. Math. Soc. 180, 327–336 (1973)Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • R. S. Doran
    • 1
  • Wayne Tiller
    • 2
  1. 1.Department of MathematicsTexas Christian UniversityFort WorthUSA
  2. 2.Structural Dynamics Research Corp.AmeliaUSA

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