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Nuclear Fréchet lattices

Part of: Topological linear spaces and related structures Ordered structures

Published online by Cambridge University Press:  01 August 2017

Antonio Fernández  and
Francisco Naranjo
Antonio Fernández
Affiliation:
Dpto. Matemática Aplicada II, Escuela Superior de Ingenieros, Camino de los Descubrimientos, s/n 41092-Sevilla, Spain e-mail: anfercar@esi.us.es
Francisco Naranjo
Affiliation:
Dpto. Matemática Aplicada II, Escuela Universitaria Politécnica, c/ Virgen de África, 7 41011-Sevilla, Spain e-mail: naranjo@platero.eup.us.es
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Abstract

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We give a characterization of nuclear Fréchet lattices in terms of lattice properties of the seminorms. Indeed, we prove that a Fréchet lattice is nuclear if and only if it is both an AL- and an AM-space.

Keywords

Fréchet latticegeneralized AL-spacesgeneralized AM-spacesnuclear spacesKöthe generalized sequences spaces

MSC classification

Secondary: 46A04: Locally convex Fréchet spaces and (DF)-spaces 46A11: Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) 46A40: Ordered topological linear spaces, vector lattices 06F30: Topological lattices, order topologies
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 72 , Issue 3 , June 2002 , pp. 409 - 418
Copyright
Copyright © Australian Mathematical Society 2002

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