Skip to main content
SpringerLink
Log in

Orthogonal Projections and Uniformly Bounded Families of Multipliers

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

For a Banach space, with a total sequence of mutually orthogonal projections, we present a criterium to verify that a family of multipliers is uniformly bounded. We assume that the Cesàro means are uniformly bounded. The results are applied to study generalized Riesz means as well as to obtain some Bernstein type inequalities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Butzer, P.L., Nessel, R.J., Trebels, W.: On summation processes of Fourier expansions in Banach spaces. I: comparison theorems. Tôhoku Math. J. 24, 127–140 (1972)

    Article  MathSciNet  Google Scholar 

  2. Butzer, P.L., Nessel, R.J., Trebels, W.: On summation processes of Fourier expansions in Banach spaces II: saturation theorems. Tôhoku Math. J. 24, 551–569 (1972)

    Article  MathSciNet  Google Scholar 

  3. Chen, W., Ditzian, Z.: Best approximation and K-functionals. Acta Math. Hungar 75(3), 165–208 (1997)

    Article  MathSciNet  Google Scholar 

  4. Dai, F.: Some equivalence theorems with K-functionals. J. Approx. Theory 121, 143–157 (2003)

    Article  MathSciNet  Google Scholar 

  5. Ditzian, Z.: Fractional derivatives and best approximation. Acta Math. Hungar. 81(4), 323–348 (1998)

    Article  MathSciNet  Google Scholar 

  6. Dickmeis, W., Nessel, R.J., Van Wickeren, E.: Steckin-type estimates for locally divisible multipliers in Banach spaces. Acta Sci. Math. 47, 169–188 (1984)

    MathSciNet  MATH  Google Scholar 

  7. Floater, M.S., Lyche, T.: Two chain rules for divided differences and Faà Di Bruno’s formula. Math. Comput. 76(258), 867–877 (2007)

    Article  Google Scholar 

  8. Görlich, E., Nessel, R.J., Trebels, W.: Bernstein-type inequalities for families of multiplier operators in Banach spaces with Cesàro decomposition: I General theory. Acta Sci. Math. (Szeged) 34(1–4), 121–130 (1973)

    MathSciNet  MATH  Google Scholar 

  9. Görlich, E., Nessel, R.J., Trebels, W.: Bernstein-type inequalities for families of multiplier operators in Banach spaces with Cesàro decomposition: II applications. Acta Sci. Math. (Szeged) 36(1–2), 39–48 (1974)

    MathSciNet  MATH  Google Scholar 

  10. Trebels, W.: Multipliers for \((C,\alpha )\)-bounded fourier expansions in Banach Spaces and approximation theory. Lecture Notes in Mathematics. Springer, Berlin (1973)

    Book  Google Scholar 

  11. Trebels, W.: Equivalence of a \(K\)-functional with the approximation behavior of some linear means for abstract Fourier series. Proc. Am. Math. Soc. 127(10), 2883–2887 (1999)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Benemérita Universidad Autónoma de Puebla, Puebla, Mexico

    Jorge Bustamante

  2. Departamento de Matemáticas, Universidad de Jaén, Jaén, Spain

    Juán J. Merino & José M. Quesada

Authors
  1. Jorge Bustamante
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Juán J. Merino
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. José M. Quesada
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jorge Bustamante.

Additional information

The JMQ is partially supported by Research Project MTM2015-67006-P.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bustamante, J., Merino, J.J. & Quesada, J.M. Orthogonal Projections and Uniformly Bounded Families of Multipliers. Results Math 73, 113 (2018). https://doi.org/10.1007/s00025-018-0875-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00025-018-0875-9

Keywords

Mathematics Subject Classification

Search

Navigation