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Paper   IPM / M / 16492
School of Mathematics
  Title:   Module operator virtual diagonals on the Fourier algebra of an inverse semigroup
  Author(s):  Massoud Amini (Joint with R. Rezavand)
  Status:   Published
  Journal: Semigroup Forum
  Vol.:  97
  Year:  2018
  Pages:   562-570
  Supported by:  IPM
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 l^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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