Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  355.40007
Autor:  Erdös, Paul; Magidor, M.
Title:  A note on regular methods of summability and the Banach-Saks property. (In English)
Source:  Proc. Am. Math. Soc. 59, 232-234 (1976).
Review:  The following theorem is proved. Let A be a regular summability matrix. Then every bounded sequence of elements in the space has a subsequence with the property that either every subsequence of this subsequence is summable by A to one and the same limit or no subsequence of this is summable by A. In the proof a result of F.Galvin and K.Prikry on partion into Borel sets [J. Symb. Logic 38, 193-198 (1973; Zbl 276.04003)] is used. A Banach space is said to possess Banach-Saks property with respect to A, if every bounded sepuence has a summable subsequence. It follows from the result above that if a Banach space has the Banach-Saks property with respect to A, then every bounded sepuence has a subsequence such that each of its subsequences is summable with respect to A.
Reviewer:  V.Ganapathy Iyer
Classif.:  * 40C05 Matrix methods in summability
                   46B15 Summability and bases in normed spaces

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag

Books Problems Set Theory Combinatorics Extremal Probl/Ramsey Th.
Graph Theory Add.Number Theory Mult.Number Theory Analysis Geometry
Probabability Personalia About Paul Erdös Publication Year Home Page