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Characterization of a class of infinite matrices with applications

Published online by Cambridge University Press:  17 April 2009

P. N. Natarajan
P. N. Natarajan
Affiliation:
Department of Mathematics, Vivekananda College, Madras – 600 004, India.
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Abstract

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In this paper, K denotes a complete, non-trivially valued, non-archimedean field. The class (lα, lα) of infininite matrices transforming sequences over K in lα to sequences in lα is characterized. Further a Mercerian theorem is proved in the context of the Banach algebra (lα, lα), α ≥ 1 and finally a Steinhaus type result is proved for the space lα. In the case of ℝ or ℀, on the other hand, the best known result so far seems to be a characterization of positive matrix transformations of the class (lα, lβ), ∞ > α ≥ β > 1.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 2 , October 1986 , pp. 161 - 175
Copyright
Copyright © Australian Mathematical Society 1986

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