Bases and quasi-reflexivity in Frechet spaces

摘要

A Frechet space E is quasi-reflexive if, either dim(E"/E) <∞, or E"[β(E", E')]/E is isomorphic to ω. A Frechet space E is totally quasi-reflexive if every separated quotient is quasi-reflexive. In this paper we show, using Schauder bases, that E is totally quasi-reflexive if and only if it is isomorphic to a closed subspace of a countable product of quasi-reflexive Banach spaces.