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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Constructive existence of Minkowski functionals


Author: Hajime Ishihara
Journal: Proc. Amer. Math. Soc. 116 (1992), 79-84
MSC: Primary 46S30; Secondary 03F65
MathSciNet review: 1089409
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Abstract: In Bishop's constructive mathematics, the framework of this paper, there are many situations where we cannot easily prove the existence of functionals whose existence is a trivial consequence of classical logic. One such functional is the Minkowski functional of a convex absorbing set. We shall prove the existence of Minkowski functionals in various spaces, and apply the theorems to establish the locatedness of the kernel of linear mappings.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1089409-9
Keywords: Minkowski functional, kernel of a linear mapping, constructive
Article copyright: © Copyright 1992 American Mathematical Society