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Highly tempering infinite matrices

  • Luis Bernal-González
  • J. Alberto ConejeroEmail author
  • Marina Murillo-Arcila
  • Juan B. Seoane-Sepúlveda
Original Paper
  • 149 Downloads

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.

Keywords

Summation method Infinite matrix Divergent sequence Toeplitz–Silverman theorem Dense linear subspace 

Mathematics Subject Classification

15B05 15A04 40C05 

Notes

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.

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Copyright information

© Springer-Verlag Italia 2017

Authors and Affiliations

  1. 1.Departamento de Análisis Matemático, Facultad de MatemáticasUniversidad de SevillaSevilleSpain
  2. 2.Instituto Universitario de Matemática Pura y AplicadaUniversitat Politècnica de ValènciaValenciaSpain
  3. 3.Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Escuela Superior de Tecnología y Ciencias ExperimentalesUniversitat Jaume ICastelló de la PlanaSpain
  4. 4.Instituto de Matemática Interdisciplinar (IMI), Departamento de Análisis Matemático, Facultad de Ciencias MatemáticasUniversidad Complutense de MadridMadridSpain

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