On the inclusion of a bounded convergence field in the space of almost convergent sequences
- 1 March 1972
- journal article
- research article
- Published by Cambridge University Press (CUP) in Glasgow Mathematical Journal
- Vol. 13 (1) , 82-90
- https://doi.org/10.1017/s0017089500001439
Abstract
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.Keywords
This publication has 2 references indexed in Scilit:
- On Sequential Cores and a Theorem of R. R. PhelpsProceedings of the American Mathematical Society, 1969
- A Property of Extreme Points of Compact Convex SetsProceedings of the American Mathematical Society, 1954