Semigroup Forum

, Volume 97, Issue 3, pp 562–570 | Cite as

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

  • Massoud Amini
  • Reza Rezavand


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).


Completely contractive Banach algebras Module operator amenability Module operator virtual diagonal Inverse semigroup Fourier algebra 


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Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Mathematical SciencesTarbiat Modares UniversityTehranIran
  2. 2.School of Mathematics, Statistics and Computer Science, College of ScienceUniversity of TehranTehranIran
  3. 3.School of MathematicsInstitute for Research in Fundamental Sciences (IPM)TehranIran

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