Fréchet spaces with no infinite-dimensional Banach quotients

We exhibit examples of Fréchet Montel spaces E which have a non-reflexive Fréchet quotient but such that every Banach quotient is finite-dimensional. The construction uses a method developed by Albanese and Moscatelli and requires new ingredients. Some of the main steps in the proof are presented in Section 2. They are of independent interest and show for example that the canonical inclusion between James spaces Jp¿Jq, 1 pJq has no infinite-dimensional Banach quotients. Plichko and Maslyuchenko had proved that it has no infinite-dimensional Banach subspaces. © 2011 Elsevier Inc.This research was partially supported by MEC and FEDER Project MTM2010-15200 and by GV Project Prometeo/2008/101.Albanese, A.; Bonet Solves, JA. (2012). Fréchet spaces with no infinite-dimensional Banach quotients. Journal of Mathematical Analysis and Applications. 387:556-567. https://doi.org/10.1016/j.jmaa.2011.09.018S55656738