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Module operator virtual diagonals on the Fourier algebra of an inverse semigroup

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Abstract

For an amenable inverse semigroup S with the set of idempotents E and a minimal idempotent, we explicitly construct a contractive and positive module operator virtual diagonal on the Fourier algebra A(S), as a completely contractive Banach algebra and operator module over \(\ell ^1(E)\). This generalizes a well known result of Zhong-Jin Ruan on operator amenability of the Fourier algebra of a (discrete) group Ruan (Am J Math 117:1449–1474, 1995).

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Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, 14115-134, Iran

    Massoud Amini

  2. School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Enghelab Avenue, Tehran, Iran

    Reza Rezavand

  3. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, 19395-5746, Iran

    Massoud Amini

Authors
  1. Massoud Amini
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  2. Reza Rezavand
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Corresponding author

Correspondence to Reza Rezavand.

Additional information

Communicated by Jerome A. Goldstein.

The first author was partly supported by a Grant from IPM (No. 90430215). The second author was partly supported by a Grant from INSF (No. 95820471).

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Amini, M., Rezavand, R. Module operator virtual diagonals on the Fourier algebra of an inverse semigroup. Semigroup Forum 97, 562–570 (2018). https://doi.org/10.1007/s00233-018-9978-6

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  • DOI: https://doi.org/10.1007/s00233-018-9978-6

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