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Some approximation problems in harmonic analysis

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Consideriamo il seguente problema: determinare quando certe algebre di Banach di funzioni sul toro o sugli interi, che sono generate dai loro idempotenti, contengono sottoalgebre chiuse che non hanno tale proprietà.

Consideriamo inoltre altre proprietà speciali che tali sottoalgebre possono possedere.

Summary

We consider the question of when certain Banach algebras on the circle group or the integers, which themselves are the closed span of their idempotents, have closed subalgebras which fail to have this property. We also consider what other special properties such subalgebras may have.

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References

  1. Bachelis G. F. andGilbert J. E.,Banach algebras on the integers with Rider subalgebras, to appear.

  2. Edwards R. E.,Fourier Series: A Modern Introduction, II. Holt, Rinehart and Winston, New York, 1967.

    Google Scholar 

  3. Friedberg S.,Closed subalgebras of group algebras. Trans. Amer. Math. Soc., 147 (1970), 117–125.

    Article  MATH  MathSciNet  Google Scholar 

  4. Kahane J.-P.,Idempotens in A(Z),Function Algebras. Scott, Foresman, Chicago (1966), 198–207.

    Google Scholar 

  5. Kahane J.-P. andKatznelson Y.,Mauvaise approximation par polynomes trigonométriques dans certaines algèbras de convolution, to appear Israel Jour. Math.

  6. Kwapien S.,On Enflo's example of a Banach space without the approximation property. Séminaire Goulaouic-Schwartz (1972–73), exposé no. VIII.

  7. Rider D.,Closed subalgebras of L1(T). Duke Math. Jour. (1969), 105–116.

  8. Rodi S.,Doctoral dissertation. University of Texas at Austin, 1976.

  9. Rudin W.,Fourier Analysis on Groups. Interscience, New York, 1962.

    MATH  Google Scholar 

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(Conferenza tenuta il 15 giugno 1978)

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Bachelis, G.F. Some approximation problems in harmonic analysis. Seminario Mat. e. Fis. di Milano 48, 119–123 (1978). https://doi.org/10.1007/BF02925566

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