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Periodica Mathematica Hungarica

, Volume 68, Issue 2, pp 143–149 | Cite as

Involutions on certain Banach algebras related to locally compact groups

  • Fatemeh Akhtari
  • Rasoul Nasr-Isfahani
Article
  • 130 Downloads

Abstract

Let \(\mathcal{{A}}\) be a Banach algebra and let \(\mathcal{{X}}\) be an introverted closed subspace of \(\mathcal{{A}}^*\). Here, we give necessary and sufficient conditions for that the dual algebra \(\mathcal{{X}}^*\) of \(\mathcal{{X}}\) or the topological centers \({\mathfrak {Z}}_t^{(1)}(\mathcal{{X}}^{*})\) and \({\mathfrak {Z}}_t^{(2)}(\mathcal{{X}}^{*})\) of \(\mathcal{{X}}^*\) are Banach \(*\)-algebras. We finally apply these results to the Banach space \(L_0^\infty (G)\) of all equivalence classes of essentially bounded functions vanishing at infinity on a locally compact group \(G\).

Keywords

Banach algebra Involution Locally compact group Topological center 

Mathematics Subject Classification

28A20 28C10 43A15 46H05 

Notes

Acknowledgments

The authors would like to thank the referee of this paper for valuable remarks. They acknowledge that this research was partially carried out at the IPM-Isfahan Branch. This research was in part supported by a grant from IPM (No. 91430417).

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2014

Authors and Affiliations

  1. 1.Department of Mathematical SciencesIsfahan University of Technology IsfahanIran
  2. 2.School of MathematicsInstitute for Research in Fundamental Sciences (IPM) TehranIran

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