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On the inclusion of a bounded convergence field in the space of almost convergent sequences

Published online by Cambridge University Press:  18 May 2009

Robert E. Atalla
Robert E. Atalla
Affiliation:
Ohio University, Athens, Ohio
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Let T = (tmn) be a regular matrix, and CTbe its bounded convergence field. Necessary and sufficient conditions for CT to contain the space of almost convergent sequences are well known. (See, e.g., [7, p.62]). G. M. Petersen has suggested as a problem for research the discovery of necessary and sufficient conditions for the reverse inclusion: When is CT contained in the space of almost convergent sequences? [7, p. 137, research problem 9]. In this paper we deal with this question in a more general context. First we need some notation.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 13 , Issue 1 , March 1972 , pp. 82 - 90
Copyright
Copyright © Glasgow Mathematical Journal Trust 1972

References

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