Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



Locating subsets of a Hilbert space

Author: Hajime Ishihara
Journal: Proc. Amer. Math. Soc. 129 (2001), 1385-1390
MSC (1991): Primary 46S30; Secondary 03F60
Published electronically: October 20, 2000
MathSciNet review: 1712901
Full-text PDF

Abstract | References | Similar Articles | Additional Information


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 [Enhancements On Off] (What's this?)

  • 1. E. Bishop and D. Bridges, Constructive Analysis, Grundlehren der math. Wiss. 279, Springer-Verlag, Berlin, 1985. MR 87d:03172
  • 2. D. Bridges and H. Ishihara, Locating the range of an operator on a Hilbert space, Bull. London Math. Soc. 24 (1992), 599-605. MR 93i:47124
  • 3. D. Bridges and H. Ishihara, A definitive constructive open mapping theorem, Math. Logic Quart. 44 (1998), 545-552. MR 99f:46009
  • 4. D. Bridges and H. Ishihara, Constructive closed range and open mapping theorems, preprint, 1998.
  • 5. D. Bridges, W. Julian, and R. Mines, A constructive treatment of open and unopen mapping theorems, Z. Math. Logik und Grundlagen der Math. Bd 35 (1989), 29-43. MR 90d:46105
  • 6. D. Bridges and F. Richman, Varieties of constructive mathematics, London Math. Soc. Lecture Notes 97, Cambridge Univ. Press, 1987. MR 88k:03127
  • 7. H. Ishihara, On the constructive Hahn-Banach theorem, Bull. London Math. Soc. 21 (1989), 79-81. MR 90a:46197
  • 8. H. Ishihara, Constructive compact operators on a Hilbert space, Ann. Pure Appl. Logic 52 (1991), 31-37. MR 92c:03066
  • 9. H. Ishihara, Constructive existence of Minkowski functionals, Proc. Amer. Math. Soc. 116 (1992), 79-84. MR 92k:46126
  • 10. F. Richman, Adjoints and the image of the ball, to appear in Proc. Amer. Math. Soc. CMP 99:17

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46S30, 03F60

Retrieve articles in all journals with MSC (1991): 46S30, 03F60

Additional Information

Hajime Ishihara
Affiliation: School of Information Science, Japan Advanced Institute of Science and Technology, Tatsunokuchi, Ishikawa 923-1292, Japan

Keywords: Constructive, locatedness, weakly totally boundedness, convexity
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.
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society