Geodesic
A Note on Convergence Fields
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 635-638

Voir la notice de l'article provenant de la source Cambridge University Press

The purpose of this note is to show that the (bounded) convergence field of a conservative matrix is closed under a certain diagonalization procedure.As an application of the above result we establish a conjecture of Hill and Sledd in (1) and obtain a result of Lorentz originally proved in (2).First we introduce some notation and definitions, most of which are standard. Let l∞ denote the Banach space of bounded sequences with the supremum norm and let c denote the closed subspace of l∞ consisting of convergent sequences. 
Berg, I. D. A Note on Convergence Fields. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 635-638. doi: 10.4153/CJM-1966-063-8
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[1] 1. Hill, J. D. and Sledd, W. T., Summability-(Z, p) and sequences of periodic type, Can. J. Math., 16 (1964), 741–754. Google Scholar

[2] 2. Lorentz, G. G., A contribution to the theory of divergent sequences, Acta Math., 80 (1948), 167–190. Google Scholar

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