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Closed graph and open mapping theorems for normed cones

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Abstract

A quasi-normed cone is a pair (X, p) such that X is a (not necessarily cancellative) cone and q is a quasi-norm on X. The aim of this paper is to prove a closed graph and an open mapping type theorem for quasi-normed cones. This is done with the help of appropriate notions of completeness, continuity and openness that arise in a natural way from the setting of bitopological spaces.

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  1. Departamento de Ciencias Matemáticas e Informática, Universidad de las Islas Baleares, Edificio Anselm Turmeda, 07122, Palma de Mallorca, Baleares, Spain

    Oscar Valero

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Valero, O. Closed graph and open mapping theorems for normed cones. Proc Math Sci 118, 245–254 (2008). https://doi.org/10.1007/s12044-008-0017-5

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  • DOI: https://doi.org/10.1007/s12044-008-0017-5

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