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A theorem on matrices and its applications in functional analysis. (English) Zbl 0538.46031
A theorem on infinite matrices of real numbers is established. The theorem can be regarded as an abstract ”sliding-hump” type result. To illustrate the usefullness of the theorem, several well-known results in functional analysis and measure theory are derived. The Orlicz-Pettis theorem and a result of Diestel and Faires on strongly additive vector measures are proved.

46G10 Vector-valued measures and integration
46A45 Sequence spaces (including Köthe sequence spaces)
46B25 Classical Banach spaces in the general theory
15A12 Conditioning of matrices
46A08 Barrelled spaces, bornological spaces
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