Consistency theorems for almost convergence

Bennett, G.; Kalton, N. J.

doi:10.1090/S0002-9947-1974-0352932-X

Consistency theorems for almost convergence
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by G. Bennett and N. J. Kalton PDF

Trans. Amer. Math. Soc. 198 (1974), 23-43 Request permission

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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