IJPAM: Volume 102, No. 3 (2015)

INVARIANT CORE FOR DOUBLE SEQUENCES
IN NON-ARCHIMEDEAN FIELDS

S. Sangeetha$^1$, V. Srinivasan$^2$
$^{1,2}$Department of Mathematics
SRM University
Kattankulathur, Chennai, 603 203, INDIA


Abstract. In this paper, $K$ denotes a complete, non-trivially valued, non-archimedean field. The entries of sequences, series and infinite matrices are in $K$. In the present paper, we prove the Knopp's core theorem for double sequences in $K$ and also the necessary and sufficient conditions for the core to be invariant under the four dimensional matrix transformation in such fields.

Received: April 2, 2015

AMS Subject Classification: 40A05, 40C05, 46S10

Key Words and Phrases: core of a double sequence, regular matrix, Knopp's core theorem, invariant core, non-archimedean fields

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DOI: 10.12732/ijpam.v102i3.9 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 102
Issue: 3
Pages: 515 - 525


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