The Sobczyk property and copies of $l_{\infty }$ in locally convex-solid Riesz spaces

Abstract.

We present a relatively short proof of the following generalization of a theorem due to Lozanovskii, Mekler and Meyer-Nieberg: A $\sigma$-Dedekind complete locally convex-solid Riesz space E contains no copy of $l_{\infty }$ iff E contains no lattice copy of $l_{\infty }$ (Theorem and Corollary 1).