Antosik, Piotr; Swartz, Charles A theorem on matrices and its applications in functional analysis. (English) Zbl 0538.46031 Stud. Math. 77, 197-205 (1984). 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. Cited in 1 Document MSC: 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 Keywords:diagonal theorem; Rosenthal’s lemma; infinite matrices; sliding-hump; Orlicz-Pettis theorem; strongly additive vector measures PDFBibTeX XMLCite \textit{P. Antosik} and \textit{C. Swartz}, Stud. Math. 77, 197--205 (1984; Zbl 0538.46031) Full Text: DOI EuDML