Constructive existence of Minkowski functionals

Ishihara, Hajime

doi:10.1090/S0002-9939-1992-1089409-9

Constructive existence of Minkowski functionals
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Proc. Amer. Math. Soc. 116 (1992), 79-84 Request permission

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.

References

Errett Bishop and Douglas Bridges, Constructive analysis, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 279, Springer-Verlag, Berlin, 1985. MR 804042, DOI 10.1007/978-3-642-61667-9
Douglas Bridges, Allan Calder, William Julian, Ray Mines, and Fred Richman, Bounded linear mappings of finite rank, J. Functional Analysis 43 (1981), no. 2, 143–148. MR 633972, DOI 10.1016/0022-1236(81)90025-2
Douglas Bridges and Hajime Ishihara, Linear mappings are fairly well-behaved, Arch. Math. (Basel) 54 (1990), no. 6, 558–562. MR 1052976, DOI 10.1007/BF01188684
Douglas Bridges and Fred Richman, Varieties of constructive mathematics, London Mathematical Society Lecture Note Series, vol. 97, Cambridge University Press, Cambridge, 1987. MR 890955, DOI 10.1017/CBO9780511565663