  The aim of this paper is to to show the admissibility of some class of
Frechet spaces (see Definition 2.3). In particular, this generalizes the main
results of [3]. As an application, we show the admissibility of a large class
modular spaces equipped with F-norms determined in Theorem 4.1. It is worth
noticing that F-norms introduced in Theorem 4.1 generalize the classical
Luxemburg F-norm. Also a linear version of admissibility (so called metric
approximation property) for order continuous symmetric spaces will be
demonstrated (see Theorem 5.1).
