×

zbMATH — the first resource for mathematics

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.

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
PDF BibTeX XML Cite
Full Text: DOI EuDML