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Almost periodic functionals on the Orlicz Figà-Talamanca Herz algebras

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Abstract

Let G be a compact group of bounded representation type. In this paper, it is shown that the space of almost periodic functionals on the Orlicz Figà-Talamanca Herz algebras \(A_\varPhi (G)\) forms a subalgebra.

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References

  1. Derighetti, A.: Convolution operators on groups. Lecture notes Un. Mat. Ital.11. Springer, Heidelberg (2011)

  2. Dunkl, C.F., Ramirez, D.E.: Subalgebras of the dual of the Fourier algebra of a compact group. Proc. Camb. Philos. Soc. 71, 329–333 (1972)

    MathSciNet  MATH  Google Scholar 

  3. Duncan, J., Ülger, A.: Almost periodic functionals on Banach algebras. Rocky Mt. J. Math. 22, 837–848 (1992)

    MathSciNet  MATH  Google Scholar 

  4. Eymard, P.: L’algèbre de Fourier d’un groupe localement compact. Bull. Soc. Math. France 92, 181–236 (1964)

    MathSciNet  MATH  Google Scholar 

  5. Filali, M., Sangani Monfared, M.: Almost periodic functionals and finite-dimensional representations. Stud. Math. 243, 329–344 (2018)

    MathSciNet  MATH  Google Scholar 

  6. Granirer, E.E.: On some spaces of linear functionals on the algebras \(A_p(G)\) for locally compact groups. Colloq. Math. 52, 119–132 (1987)

    MathSciNet  MATH  Google Scholar 

  7. Herz, C.: Harmonic synthesis for subgroups. Ann. Inst. Fourier 23(3), 91–123 (1973)

    MathSciNet  MATH  Google Scholar 

  8. Hewitt, E., Ross, K.A.: Abstract harmonic analysis II. Springer, Berlin (1970)

    MATH  Google Scholar 

  9. Köthe, G.: Topological vector spaces I. Springer-Verlag, New York (1969)

    MATH  Google Scholar 

  10. Lau, A.T.M., Wong, J.C.S.: Weakly almost periodic elements in \(L_\infty (G)\) of a locally compact group. Proc. Am. Math. Soc. 107, 1031–1036 (1989)

    MATH  Google Scholar 

  11. Megginson, R.E.: An introduction to Banach space theory. Springer, New York (1998)

    MATH  Google Scholar 

  12. Moore, C.C.: Groups with finite dimensional irreducible representations. Trans. Am. Math. Soc. 166, 401–410 (1972)

    MathSciNet  MATH  Google Scholar 

  13. Sangani Monfared, M.: On almost periodic functionals on the Figà-Talamanca–Herz alegbras \( A_p(G)\). J. Nonlinear Var. Anal. 1, 325–331 (2017)

    MATH  Google Scholar 

  14. Lal, R., Kumar, N.S.: Orlicz Figà-Talamanca Herz algebras and invariant means. Indag. Math. 30, 340–354 (2019)

    MathSciNet  MATH  Google Scholar 

  15. Rao, M.M., Ren, Z.D.: Theory of Orlicz spaces. Dekker, New York (1991)

    MATH  Google Scholar 

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Acknowledgements

Both the authors would like to thank the unknown referee for meticulously reading the paper and giving us valuable suggestions. The authors would also like to thank Prof. N. Shravan Kumar for his moral support. This article was supported by University Grants Commission (Grant Numbers 416809, 415846).

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Delhi, Delhi, 110016, India

    Rattan Lal & Manoj Kumar

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  1. Rattan Lal
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  2. Manoj Kumar
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Correspondence to Rattan Lal.

Additional information

Communicated by Nico Spronk.

Both the authors thank the University Grants Commission, India, for the research grant.

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Lal, R., Kumar, M. Almost periodic functionals on the Orlicz Figà-Talamanca Herz algebras. Adv. Oper. Theory 5, 1580–1587 (2020). https://doi.org/10.1007/s43036-020-00070-w

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  • DOI: https://doi.org/10.1007/s43036-020-00070-w

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