Submatrices of four dimensional summability matrices

Fatih Nuray; Richard F. Patterson

doi:10.4067/S0719-06462015000200006

Authors

Fatih Nuray Department of Mathematics, AfyonKocatepe University, Afyonkarahisar, Turkey. Deparment of Mathematics and Statistics, University of North Florida, Jacksonville, FL, USA University of North Florida, Jacksonville, FL, USA
Richard F. Patterson Department of Mathematics and Statistics, University of North Florida Jacksonville, Florida, 32224

DOI:

https://doi.org/10.4067/S0719-06462015000200006

Keywords:

Submatrix, four dimensional summability matrix, Double Sequences, Pringsheim Limit, RH-regular matrix

Abstract

In this paper, we show that a matrix that maps l”²”² into l”²”² can be obtained from any RH-regular matrix by the deletion of rows. Also a four dimensional conservative matrix can be obtained by the deletion of rows from a matrix that preserves boundedness. We will use these techniques to derive a sufficient condition for a four dimensional matrix to sum an unbounded sequence.