A strong open mapping theorem for surjections from cones onto Banach spaces

DOI10.1016/j.aim.2014.03.008zbMath1301.46001arXiv1302.2822OpenAlexW2091557044MaRDI QIDQ2450097

Miek Messerschmidt, M. F. E. de Jeu

Publication date: 16 May 2014

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.2822

zbMATH Keywords

coneBanach spaceopen mapping theoremordered Banach spacebounded continuous right inverse

Mathematics Subject Classification ID

Open mapping and closed graph theorems; completeness (including (B)-, (B_r)-completeness) (46A30) Ordered normed spaces (46B40)

Related Items (10)

On the Bonsall cone spectral radius and the approximate point spectrum ⋮ Lower spectral radius and spectral mapping theorem for suprema preserving mappings ⋮ A pointwise Lipschitz selection theorem ⋮ Normality of spaces of operators and quasi-lattices ⋮ A surjective summation operator with no Lipschitz right inverse ⋮ The Riesz Space of Minimal Usco Maps ⋮ Uniform boundedness principle for nonlinear operators on cones of functions ⋮ Riesz-Kantorovich formulas for operators on multi-wedged spaces ⋮ Geometric duality theory of cones in dual pairs of vector spaces ⋮ Strong Klee-Andô theorems through an open mapping theorem for cone-valued multi-functions

Cites Work

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• Positive one-parameter semigroups on ordered Banach spaces
• Boundedness and continuity of linear functionals
• Closed graph and open mapping theorems for normed cones
• Ordered vector sequence spaces and related classes of linear operators
• On fundamental properties of a Banach space with a cone
• Spaces of Linear Operators between Partially Ordered Banach Spaces
• DOMINATED EXTENSIONS OF CONTINUOUS AFFINE FUNCTIONS WITH RANGE AN ORDERED BANACH SPACE
• Paracompactness and product spaces

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