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\(\varphi \)-Biprojectivity of Banach Algebras with Applications to Hypergroup Algebras

  • Morteza Essmaili
  • Alireza R. Medghalchi
  • Ramin Ramezani
Original Paper

Abstract

At the present paper, we study the notions of \(\varphi \)-biprojectivity, \(\varphi \)-Johnson contractibility, and \(\varphi \)-contractibility of Banach algebras, where \(\varphi \) is a nonzero character. We introduce the condition (Q) which is weaker than \(\varphi \)-biprojectivity. For classes of Banach algebras with a left and right approximate identity, we obtain some relations between these notions. Moreover, we apply these results for the hypergroup algebra \(L^{1}(K)\) and some Segal algebras with respect to the \(L^{1}(K)\). As a main result, for a hypergroup K,  we prove that the hypergroup algebra \(L^{1}(K)\) is \(\varphi \)-biprojective (left \(\varphi \)-contractible) if and only if K is compact.

Keywords

Hypergroup algebras \(\varphi \)-Biprojectivity \(\varphi \)-Contractibility \(\varphi \)-Johnson contractibility Abstract Segal algebras 

Mathematics Subject Classification

Primary 43A20 Secondary 43A22 

Notes

Acknowledgements

The first author was partially supported by a grant from IPM (no. 94470069).

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Copyright information

© Iranian Mathematical Society 2018

Authors and Affiliations

  • Morteza Essmaili
    • 1
    • 2
  • Alireza R. Medghalchi
    • 1
  • Ramin Ramezani
    • 1
  1. 1.Department of Mathematics, Faculty of Mathematical and Computer SciencesKharazmi UniversityTehranIran
  2. 2.School of MathematicsInstitute for Research in Fundamental Sciences (IPM)TehranIran

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