Locating subsets of a Hilbert space
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- by Hajime Ishihara PDF
- Proc. Amer. Math. Soc. 129 (2001), 1385-1390 Request permission
Abstract:
This paper deals with locatedness of convex subsets in inner product and Hilbert spaces which plays a crucial role in the constructive validity of many important theorems of analysis.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 and Hajime Ishihara, Locating the range of an operator on a Hilbert space, Bull. London Math. Soc. 24 (1992), no. 6, 599–605. MR 1183317, DOI 10.1112/blms/24.6.599
- Douglas Bridges and Hajime Ishihara, A definite constructive open mapping theorem?, MLQ Math. Log. Q. 44 (1998), no. 4, 545–552. MR 1654328, DOI 10.1002/malq.19980440413
- D. Bridges and H. Ishihara, Constructive closed range and open mapping theorems, preprint, 1998.
- Douglas Bridges, William Julian, and Ray Mines, A constructive treatment of open and unopen mapping theorems, Z. Math. Logik Grundlag. Math. 35 (1989), no. 1, 29–43. MR 982701, DOI 10.1002/malq.19890350105
- 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
- Hajime Ishihara, On the constructive Hahn-Banach theorem, Bull. London Math. Soc. 21 (1989), no. 1, 79–81. MR 967795, DOI 10.1112/blms/21.1.79
- Hajime Ishihara, Constructive compact operators on a Hilbert space, Ann. Pure Appl. Logic 52 (1991), no. 1-2, 31–37. International Symposium on Mathematical Logic and its Applications (Nagoya, 1988). MR 1104052, DOI 10.1016/0168-0072(91)90037-M
- Hajime Ishihara, Constructive existence of Minkowski functionals, Proc. Amer. Math. Soc. 116 (1992), no. 1, 79–84. MR 1089409, DOI 10.1090/S0002-9939-1992-1089409-9
- F. Richman, Adjoints and the image of the ball, to appear in Proc. Amer. Math. Soc.
Additional Information
- Hajime Ishihara
- Affiliation: School of Information Science, Japan Advanced Institute of Science and Technology, Tatsunokuchi, Ishikawa 923-1292, Japan
- Email: ishihara@jaist.ac.jp
- Received by editor(s): February 26, 1999
- Received by editor(s) in revised form: July 30, 1999
- Published electronically: October 20, 2000
- Additional Notes: This research was partly supported by a Grant-in-Aid for Scientific Research (C) No.09640253 of the Ministry of Education, Science, Sports and Culture.
- Communicated by: Carl G. Jockusch, Jr.
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1385-1390
- MSC (1991): Primary 46S30; Secondary 03F60
- DOI: https://doi.org/10.1090/S0002-9939-00-05674-4
- MathSciNet review: 1712901