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Cauchy multiplication of Euler summable series in ultrametric fields

Deepa R., Natarajan P. N., Srinivasan V.

Commentationes Mathematicae

2013

Vol 53, No. 1

73--79

Euler summability method in a complete, non-trivially valued, ultrametric field of the characteristic zero was introduced by Natarajan in [7]. Some properties of the Euler summability method in such fields were studied in [2] and [7]. The purpose of the present note is to continue the study and to prove a pair of theorems on the Cauchy product of Euler summable sequences and series.

An addendum to the paper “Some characterizations of Schur matrices in ultrametric fields”

Natarajan P. N.

Commentationes Mathematicae

2013

Vol 53, No. 1

81--82

In this short note, we add a few remarks in the context of [1].

Some characterizations of Schur matrices in ultrametric fields

Natarajan P.N.

Commentationes Mathematicae

2012

Vol. 52, [Z] 2

137--142

In this short paper, K denotes a complete, non-trivially valued, ultra-metric field. Sequences and infinite matrices have entries in K. We prove a few characterizations of Schur matrices in K. We then deduce some non-inclusion theorems modelled on the results of Agnew [1] and Fridy [3] in the classical case.

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.