This is an announcement for the paper "Rainwater-Simons-type convergence theorems for generalized convergence methods" by Jan-David Hardtke.

Abstract: We extend the well-known Rainwater-Simons convergence theorem to various generalized convergence methods such as strong matrix summability, statistical convergence and almost convergence. In fact we prove these theorems not only for boundaries but for the more general notion of (I)-generating sets introduced by Fonf and Lindenstrauss.

Archive classification: math.FA

Mathematics Subject Classification: 46B20, 40C05, 40C99

Remarks: 11 pages

Submitted from: hardtke@math.fu-berlin.de

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1011.2365

or

http://arXiv.org/abs/1011.2365