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José BONET & José A. Conojero

Duality for Monomorphisms and Almost Open Operators Between Locally Convex Spaces

(Volume 70 - Année 2001 — Numéro 4 - 5 - 6)
Article
Open Access
Mots-clés : Locally convex spaces, monomorphisms, almost open operators, Frechet spaces, (DF)-spaces

Abstract

A continuous and linear operator T : EF between Banach spaces E and F is a bounded below, resp. surjective (and open), if and only if its transposed operator T’ : F’b E’b is surjective (and open), resp. bounded below.  This survey paper presents a complete analysis of the possible extensions of these two results when E and F are both Fréchet spaces or both complete (DF)-spaces.


1Mathematics Subject Classification 22000 : 47A05, 46A04

To cite this article

José BONET & José A. Conojero, «Duality for Monomorphisms and Almost Open Operators Between Locally Convex Spaces», Bulletin de la Société Royale des Sciences de Liège [En ligne], Volume 70 - Année 2001, Numéro 4 - 5 - 6, 183 – 193 URL : https://popups.uliege.be/0037-9565/index.php?id=1839.

About: José BONET

Departamento de Matemática Aplicada, ETS Arquitectura, Universidad Politécnica de Valencia, E-46071 Valencia, Spain, jbonet@mat.upv.es

About: José A. Conojero

Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica de Valencia, E·46071 Valencia, Spain, aconejero@mat.upv.es