Submatrices of Four Dimensional Summability Matrices

Fatih Nuray¹ y Richard F. Patterson^2
1 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 fnuray@aku.edu.tr
² Department of Mathematics and Statistics, University of North Florida Jacksonville, Florida, 32224 rpatters@unf.edu

ABSTRACT
In this paper, we show that a matrix that maps ℓ′′ into ℓ′′ 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.

Keywords and Phrases: Submatrix, four dimensional summability matrix, Double Sequences, Pringsheim Limit, RH-regular matrix
2010 AMS Mathematics Subject Classification: 40C05, 40D05.

RESUMEN
En este trabajo probamos que una matriz que lleva ℓ′′ en ℓ′′ se puede obtener a partir de cualquier matriz RH-regular eliminando filas. También una matriz cuatro dimensional conservative se puede obteber eliminando filas en una matriz que preserva acotación. Usamos estas técnicas para encontrar una condici´on suficiente para que una matriz cuatro dimensional sume una sucesi´on no acotada.

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Received: January 2014. Accepted: January 2015.