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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Consistency theorems for almost convergence


Authors: G. Bennett and N. J. Kalton
Journal: Trans. Amer. Math. Soc. 198 (1974), 23-43
MSC: Primary 46A45
DOI: https://doi.org/10.1090/S0002-9947-1974-0352932-X
MathSciNet review: 0352932
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Abstract: The concept of almost convergence of a sequence of real or complex numbers was introduced by Lorentz, who developed a very elegant theory. The purpose of the present paper is to continue Lorentz's investigations and obtain consistency theorems for almost convergence; this is achieved by studying certain locally convex topological vector spaces.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0352932-X
Keywords: Banach limit, almost convergence, topological sequence space, FK-space, matrix transformation, consistency theorems, superconvergence in topological vector spaces
Article copyright: © Copyright 1974 American Mathematical Society