Highly tempering infinite matrices
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.
KeywordsSummation method Infinite matrix Divergent sequence Toeplitz–Silverman theorem Dense linear subspace
Mathematics Subject Classification15B05 15A04 40C05
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.