WAP-biprojectivity of the enveloping dual Banach algebras

  • S. F. Shariati
  • A. PourabbasEmail author
  • A. Sahami


In this paper, we introduce a new notion of biprojectivity, called WAP-biprojectivity for \(F(\mathcal {A})\), the enveloping dual Banach algebra associated to a Banach algebra \(\mathcal {A}\). We find some relations between Connes biprojectivity, Connes amenability and this new notion. We show that, for a given dual Banach algebra \(\mathcal {A}\), if \(F(\mathcal {A})\) is Connes amenable, then \(\mathcal {A}\) is Connes amenable. For an infinite commutative compact group G, we show that the convolution Banach algebra \(F(L^2(G))\) is not WAP-biprojective. Finally, we provide some examples of the enveloping dual Banach algebras and we study their WAP-biprojectivity and Connes amenability.


Enveloping dual Banach algebra WAP-biprojective Connes amenable Connes biprojective 

Mathematics Subject Classification

Primary 46M10 46H20 Secondary 46H25 43A10 



The authors are grateful to the referee for his/her kind suggestions for a better presentation of the manuscript.


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Copyright information

© Unione Matematica Italiana 2019

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceAmirkabir University of TechnologyTehranIran
  2. 2.Department of Mathematics, Faculty of Basic ScienceIlam UniversityIlamIran

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