Convergent subseries of s ℐ -convergent series

Abstract

We say that an ideal ℐ has property (T) if for every ℐ-convergent series $$ {\sum}_{n=1}^{\infty }{x}_n, $$ there exists a set A ∈ ℐ such that Σn∈ℕ\A xn converges in the usual sense. The aim of this paper is to construct a nontrivial ideal with property (T) under the assumption that cov (ℳ) = c.