Some characterizations of Schur matrices in ultrametric fields

• Autorzy: Natarajan P.N.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

ultrametric field; regular matrix; Schur matrix; non-inclusion theorem; Steinhaus theorem

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2012
• Tom: Vol. 52, [Z] 2
• Strony: 137--142
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Natarajan P.N.

• Old No. 2/3, New No. 3/3, Second Main Road, R.A. Puram, Chennai 600 028,India

Bibliografia

• [1] R.P. Agnew, A simple sufficient condition that a method of summability be stronger than convergence, Bull. Amer. Math. Soc. 52 (1946), 128 132.
• [2] G. Bachman, Introduction to p-adic numbers and valuation theory, Academic Press (1964).
• [3] J.A. Fridy, Non-inclusion theorems for summability matrices, Int. J. Math. & Math. Sci. 20 (1997), 511-516.
• [4] A.F. Monna,Sur le theoreme de Banach-Steinhaus, Indag. Math. 25 (1963), 121-131.
• [5] P.N. Natarajan, The Steinhaus theorem for Toeplitz matrices in non-archimedean fields, Comment. Math. Prace Mat. 20 (1978), 417 422.
• [6] P.N. Natarajan and V. Srinivasan, Silverman-Toeplitz theorem for double sequences and series and its application to Norlund means in non-archimedean fields, Ann. Math. Blaise Pascal 9 (2002), 85-100.