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The Schur and Steinhaus Theorems for 4-Dimensional Infinite Matrices

Natarajan P. N.

Commentationes Mathematicae

2014

Vol 54, No. 2

159--165

This paper is a sequel to [2]. Throughout this paper, entries of double sequences, double series and 4-dimensional infinite matrices are real or complex numbers. We prove the Schur and Steinhaus theorems for 4-dimensional infinite matrices.

The Schur and Steinhaus Theorems for 4-Dimensional Matrices in Ultrametric Fields

Natarajan P.N.

Commentationes Mathematicae

2011

Vol. 51, [Z] 2

203-209

Throughout this paper, K denotes a ds-complete, non-trivially valued, ultrametric field. Entries of double sequences, double series and 4-dimensional matrices are in K. We prove the Schur and Steinhaus theorems for 4-dimensional matrices in such fields.