Rate preservation of double sequences under \(l\)-\(l\) type transformation (Q1608214)

Summary: Following the concepts of divergent rate preservation for ordinary sequences, we present a notion of rates preservation of divergent double sequences under \(l\)-\(l\) type transformations. Definitions for Pringsheim limit inferior and superior are also presented. These definitions and the notion of asymptotically equivalent double sequences, are used to present necessary and sufficient conditions on the entries of a four-dimensional matrix such that the rate of divergence is preserved for a given double sequence under \(l\)-\(l\) type mapping where \(l=: \{x_{k,l}:\sum _{k,l=1,1}^{\infty,\infty} |x_{k,l}|< \infty\}\).