Skip to main content
SpringerLink
Log in

Highly tempering infinite matrices

  • Original Paper
  • Published:
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this short note, it is proved the existence of infinite matrices that not only preserve convergence and limits of sequences but also convert every member of some dense vector space consisting, except for zero, of divergent sequences, into a convergent sequence.

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. Aizpuru, A., Pérez-Eslava, C., Seoane-Sepúlveda, J.B.: Linear structure of sets of divergent sequences and series. Linear Algebra Appl. 418(2–3), 595–598 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  2. Aron, R.M., Bernal-González, L., Pellegrino, D., Seoane-Sepúlveda, J.B.: Lineability: The Search for Linearity in Mathematics. Monographs and Research Notes in Mathematics. Chapman & Hall/CRC, Boca Raton, FL (2016)

    MATH  Google Scholar 

  3. Aron, R.M., Gurariy, V.I., Seoane-Sepúlveda, J.B.: Lineability and spaceability of sets of functions on \({\mathbb{R}}\). Proc. Am. Math. Soc. 133(3), 795–803 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bernal-González, L., Pellegrino, D., Seoane-Sepúlveda, J.B.: Linear subsets of nonlinear sets in topological vector spaces. Bull. Am. Math. Soc. (N.S.) 51(1), 71–130 (2014). doi:10.1090/S0273-0979-2013-01421-6

    Article  MathSciNet  MATH  Google Scholar 

  5. Gámez-Merino, J.L., Seoane-Sepúlveda, J.B.: An undecidable case of lineability in \({\mathbb{R}}^{\mathbb{R}}\). J. Math. Anal. Appl. 401(2), 959–962 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gelbaum, B.R., Olmsted, J.M.H.: Counterexamples in Analysis. Dover Publications Inc., Mineola, NY (2003)

    MATH  Google Scholar 

  7. Horváth, J.: Topological Vector Spaces and Distributions, vol. I. Addison-Wesley, Reading, MA (1966)

    MATH  Google Scholar 

  8. Peyerimhoff, A.: Lectures on Summability. Lecture Notes in Mathematics. Springer, Berlin (1970)

    MATH  Google Scholar 

  9. Kuratowski, K., Mostowski, A.: Set Theory. North Holland, Amsterdam (1976)

    MATH  Google Scholar 

  10. Wilansky, A.: Summability Through Functional Analysis. North-Holland, Amsterdam (1984)

    MATH  Google Scholar 

Download references

Acknowledgements

The first author has been supported by the Plan Andaluz de Investigación de la Junta de Andalucía FQM-127 Grant P08-FQM-03543 and by MEC Grant MTM2015-65242-C2-1-P. The second and third authors have been supported by MEC, Grant MTM2016-75963-P. The fourth author has been supported by Grant MTM2015-65825-P.

Author information

Authors and Affiliations

  1. Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, Avenida Reina Mercedes, 41080, Seville, Spain

    Luis Bernal-González

  2. Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022, Valencia, Spain

    J. Alberto Conejero

  3. Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Escuela Superior de Tecnología y Ciencias Experimentales, Universitat Jaume I, Campus de Ríu Sec, 12071, Castelló de la Plana, Spain

    Marina Murillo-Arcila

  4. Instituto de Matemática Interdisciplinar (IMI), Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, Madrid, 28040, Spain

    Juan B. Seoane-Sepúlveda

Authors
  1. Luis Bernal-González
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Alberto Conejero
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marina Murillo-Arcila
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Juan B. Seoane-Sepúlveda
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Alberto Conejero.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bernal-González, L., Conejero, J.A., Murillo-Arcila, M. et al. Highly tempering infinite matrices. RACSAM 112, 341–345 (2018). https://doi.org/10.1007/s13398-017-0385-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13398-017-0385-8

Keywords

Mathematics Subject Classification

Search

Navigation